Convex optimization

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Convex optimization has applications in a wide range of disciplines, such as automatic control systems, estimation and signal processing, communications and networks, electronic circuit design, data analysis and modeling, finance, statistics (optimal experimental design), and structural optimization, where the approximation concept has proven to be efficient.
With recent advancements in computing and optimization algorithms, convex programming is nearly as straightforward as linear programming.
Definition.
A convex optimization problem is an optimization problem in which the objective function is a convex function and the feasible set is a convex set. A function formula_1 mapping some subset of formula_2into formula_3 is convex if its domain is convex and for all formula_4 and all formula_5 in its domain, the following condition holds: formula_6. A set S is convex if for all members formula_7 and all formula_4, we have that formula_9.
Concretely, a convex optimization problem is the problem of finding some formula_10 attaining
where the objective function formula_12 is convex, as is the feasible set formula_13.
 If such a point exists, it is referred to as an "optimal point" or "solution"; the set of all optimal points is called the "optimal set". If formula_1 is unbounded below over formula_13 or the infimum is not attained, then the optimization problem is said to be "unbounded". Otherwise, if formula_13 is the empty set, then the problem is said to be "infeasible".
Standard form.
A convex optimization problem is in "standard form" if it is written as
where:
This notation describes the problem of finding formula_18 that minimizes formula_28 among all formula_29 satisfying formula_30, formula_21 and formula_32, formula_23. The function formula_1 is the objective function of the problem, and the functions formula_35 and formula_36 are the constraint functions.
The feasible set formula_13 of the optimization problem consists of all points formula_38 satisfying the constraints. This set is convex because formula_39 is convex, the sublevel sets of convex functions are convex, affine sets are convex, and the intersection of convex sets is convex.
A solution to a convex optimization problem is any point formula_40 attaining formula_11. In general, a convex optimization problem may have zero, one, or many solutions.
Many optimization problems can be equivalently formulated in this standard form. For example, the problem of maximizing a concave function formula_1 can be re-formulated equivalently as the problem of minimizing the convex function formula_43. The problem of maximizing a concave function over a convex set is commonly called a convex optimization problem.
Properties.
The following are useful properties of convex optimization problems:
These results are used by the theory of convex minimization along with geometric notions from functional analysis (in Hilbert spaces) such as the Hilbert projection theorem, the separating hyperplane theorem, and Farkas' lemma.
Applications.
The following problem classes are all convex optimization problems, or can be reduced to convex optimization problems via simple transformations:
Convex optimization has practical applications for the following.
Lagrange multipliers.
Consider a convex minimization problem given in standard form by a cost function formula_44 and inequality constraints formula_45 for formula_46. Then the domain formula_47 is:
The Lagrangian function for the problem is
For each point formula_50 in formula_51 that minimizes formula_1 over formula_51, there exist real numbers formula_54 called Lagrange multipliers, that satisfy these conditions simultaneously:
If there exists a "strictly feasible point", that is, a point formula_61 satisfying
then the statement above can be strengthened to require that formula_63.
Conversely, if some formula_50 in formula_51 satisfies (1)–(3) for scalars formula_66 with formula_63 then formula_50 is certain to minimize formula_1 over formula_51.
Algorithms.
Unconstrained convex optimization can be easily solved with gradient descent (a special case of steepest descent) or Newton's method, combined with line search for an appropriate step size; these can be mathematically proven to converge quickly, especially the latter method. Convex optimization with linear equality constraints can also be solved using KKT matrix techniques if the objective function is a quadratic function (which generalizes to a variation of Newton's method, which works even if the point of initialization does not satisfy the constraints), but can also generally be solved by eliminating the equality constraints with linear algebra or solving the dual problem. Finally, convex optimization with both linear equality constraints and convex inequality constraints can be solved by applying an unconstrained convex optimization technique to the objective function plus logarithmic barrier terms. (When the starting point is not feasible - that is, satisfying the constraints - this is preceded by so-called "phase I" methods, which either find a feasible point or show that none exist. Phase I methods generally consist of reducing the search in question to yet another convex optimization problem.)
Convex optimization problems can also be solved by the following contemporary methods:
Subgradient methods can be implemented simply and so are widely used. Dual subgradient methods are subgradient methods applied to a dual problem. The drift-plus-penalty method is similar to the dual subgradient method, but takes a time average of the primal variables.
Software.
There is a large software ecosystem for convex optimization. This ecosystem has two main categories: "solvers" on the one hand and "modeling tools" (or "interfaces") on the other hand.
Solvers implement the algorithms themselves and are usually written in C. They require users to specify optimization problems in very specific formats which may not be natural from a modeling perspective. Modeling tools are separate pieces of software that let the user specify an optimization in higher-level syntax. They manage all transformations to and from the user's high-level model and the solver's input/output format.
The table below shows a mix of modeling tools (such as CVXPY and Convex.jl) and solvers (such as CVXOPT and MOSEK). This table is by no means exhaustive.
Extensions.
Extensions of convex optimization include the optimization of biconvex, pseudo-convex, and quasiconvex functions. Extensions of the theory of convex analysis and iterative methods for approximately solving non-convex minimization problems occur in the field of generalized convexity, also known as abstract convex analysis.


Luch Design Bureau

Luch Design Bureau , located in Kyiv, Ukraine, is a major Ukrainian developer of components for the defense industry.
The company is in close co-operation with the Artem holding company, also located in Kyiv. Artem is the main manufacturer of the models developed by the Luch Design Bureau.
The company was first established in Ukraine in 1965 and quickly became a leading Soviet developer of automated control systems and diagnostics systems in aviation engineering.
History.
1965 – development and release for production of PPP-3SM mobile position of preliminary preparation for application (with its location on UAZ car chassis) with air-to-air missiles manual control and PPP-3SAM mobile position of preliminary preparation for application with missiles automatic control system as a basis for creation of further missile automatic control systems for the Air and Navy Forces.
1965-1969 – creation and release for production of SAK-46 automatic control system for control of air missiles and automatic control and AKIPS-80 test mobile station for control of anti-submarine missiles. In the Soviet Union the mentioned developments were recognized as a first automatic control systems by the State Commissions.
1968-1972 – development and release for production of “Ingul” system (with its location on GAZ-66 car chassis) for preparation for application and maintenance of 9 types of air missiles.
1968-1977 – development and release for production of automatic test and control mobile stations:
- AKIPS-125 for underwater missiles control;
- AKIPS-4U for  anti-submarine missiles control;
- AKIPS-4U1 for torpedoes control.
1969-1977 – development and release for production of “Trubezh” system for preparation for application and maintenance of 12 types of air missiles.
1975-1977 – creation of current information aircraft recorder - RIU.
1977-1980 – development and release for production of “Ingul-A” and “Trubezh-A” systems with use of modularity (container) equipment construction for preparation for application and control of 26 types of missiles and guided air bombs (“Ingul-A”) and 18 types of missiles (“Trubezh-A”).
1978-1989 – development and release for production of automatic control and test mobile stations AKIPS-1 and AKIPS-3.2 for control of air anti-submarine missiles.
All mentioned stations were put into service by the Armed Forces of the Soviet Union and a number of foreign countries.
1981-1983 – development and release for production of multipurpose modular “Gurt” system which provides the preparation for application of more than 40 types of missiles and their various modifications. The “Gurt” system replaced “Ingul” and “Trubezh” systems that were in service.
In addition to new equipment samples development SKDB “Luch” is actively engaged in modernization and overhaul-period renewal of existing equipment.
By the respective coordinated decisions of the ministries of Ukraine the SKDB “Luch” was assigned as a Principal enterprise of Ukraine that conducts and coordinate works on specified life cycle and  lifetime prolongation of air, anti-aircraft missiles, mine and torpedo weapon, the “Ingul” and “Gurt” systems as well as AKIPS stations.
Since 1979 SKDB “Luch” has been developing and producing units of servo electric control surface actuators of control systems of air, anti-aircraft missiles and torpedoes. More than ten steering modules with electric actuators were developed for products of various classes which according to their characteristics are highly competitive with the best world analogs.
Thus, for example, in 1986 the block of servo electric control surface actuators for R-77 air-to-air missile with lattice control surfaces was created. On the basis of the compact commutatorless electric motors created in Ukraine for the previous decade the SKDB “Luch” developed and has been producing a number of small-sized units of servo electric control surface actuators for the guided tank missiles. Actuators are a part of developed and produced by the SKDB “Luch” digital control systems which provide rounds and missiles precise guidance. Actuators provide high accuracy characteristics, have increased jamming resistance and withstand overloads which take place during firing from guns.
Since 2002 the SKDB “Luch” has been supplying (instead of the “Gurt” system) the “Gurt-M” system which provides:
- control and preparation for application of more than 50 various modifications of air missiles and guided air bombs;
- final checking of missiles at manufacturing plants;
- fault diagnostic during missiles repair;
- missiles technical state forecast during overhaul-period renewal.
More recently the SKDB “Luch” has been a Principal enterprise that develops conceptually new special military equipment for Ukraine with participation of over than 30 Ukrainian enterprises. Products developed under this program are included in the top-priority category.
Products.

List of products


Enterprise appliance transaction module

An enterprise appliance transaction module (EATM) is a device, typically used in the manufacturing automation marketplace, for the transfer of plant floor equipment and product status to manufacturing execution systems (MES), enterprise resource planning (ERP) systems and the like.
Solutions that deliver manufacturing floor integration have evolved over time. Initially they took the form of custom integrated systems, designed and delivered by system integrators. These solutions were largely based on separate commercial off-the-shelf (COTS) products integrated into a custom system.
Modern EATM products might not needing any software development or custom integration.
Components.
Hardware platform – embedded computer, computer appliance
Device communications software – Support for the automation protocols from which data will be extracted. Device communications software typically operates through polled or change based protocols that are vendor specific. Data to be extracted is typically organized into related items, and transferred based on a machine status such as Cycle Complete, Job Start, System Downtime Event, Operator Change, etc.
Typical protocols; Rockwell Automation CIP, ControlLogix backplane, EtherNet/IP, Siemens Industrial Ethernet, Modbus TCP. There are hundreds of automation device protocols and EATM solutions are typically targeting certain market segments and will be based on automation vendor relationships.
Enterprise communications software – Software that will enable communications to enterprise systems. Communications at this level are typically transaction oriented and require data transactions to be sent and acknowledged to ensure the data integrity. Examples include; Relational Database Adapters, Java Message Services (JMS), Oracle Database Interfaces and proprietary interfaces to specific products.
Transaction application – Software that is configured to watch and collect device variables, formats them into required transactions, and transfer the results securely and reliably to other systems. The transaction application resides between the device communications and enterprise communications.
Overall, a manufacturing environment is portrayed as a three layer manufacturing pyramid. At the base, device control Systems – Programmable Logic Controller (PLC) and Supervisory Control and Data Acquisition systems (SCADA) perform the process automation functions. A layer above that encompasses Plant Execution Systems that deliver the functions of; Asset Management, Genealogy, statistical process control (SPC]) MES, order tracking, quality assurance and scheduling. At the top most level, enterprise resource planning (ERP) systems offer final control over the enterprise and track overall enterprise performance.
It is the job of EATM to act as a bi-directional bridge between field devices and the supervisory control systems. These field devices could be located in a work cell or an assembly or process line. They could be very simple devices, or programmable controllers, machine controls, or PLCs. The upstream business systems could be ANDON and Kanban systems for that line, manufacturing execution systems (MES), and archival quality databases.


Nyquist stability criterion

In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer at Siemens in 1930 and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, is a graphical technique for determining the stability of a dynamical system.
Because it only looks at the Nyquist plot of the open loop systems, it can be applied without explicitly computing the poles and zeros of either the closed-loop or open-loop system (although the number of each type of right-half-plane singularities must be known). As a result, it can be applied to systems defined by non-rational functions, such as systems with delays. In contrast to Bode plots, it can handle transfer functions with right half-plane singularities. In addition, there is a natural generalization to more complex systems with multiple inputs and multiple outputs, such as control systems for airplanes.
The Nyquist stability criterion is widely used in electronics and control system engineering, as well as other fields, for designing and analyzing systems with feedback. While Nyquist is one of the most general stability tests, it is still restricted to linear time-invariant (LTI) systems. Nevertheless, there are generalizations of the Nyquist criterion (and plot) for non-linear systems, such as the circle criterion and the scaled relative graph of a nonlinear operator. Additionally, other stability criteria like Lyapunov methods can also be applied for non-linear systems.
Although Nyquist is a graphical technique, it only provides a limited amount of intuition for why a system is stable or unstable, or how to modify an unstable system to be stable. Techniques like Bode plots, while less general, are sometimes a more useful design tool.
Nyquist plot.
A Nyquist plot is a parametric plot of a frequency response used in automatic control and signal processing. The most common use of Nyquist plots is for assessing the stability of a system with feedback. In Cartesian coordinates, the real part of the transfer function is plotted on the "X"-axis while the imaginary part is plotted on the "Y"-axis. The frequency is swept as a parameter, resulting in one point per frequency. The same plot can be described using polar coordinates, where gain of the transfer function is the radial coordinate, and the phase of the transfer function is the corresponding angular coordinate. The Nyquist plot is named after Harry Nyquist, a former engineer at Bell Laboratories.
Assessment of the stability of a closed-loop negative feedback system is done by applying the Nyquist stability criterion to the Nyquist plot of the open-loop system (i.e. the same system without its feedback loop). This method is easily applicable even for systems with delays and other non-rational transfer functions, which may appear difficult to analyze with other methods. Stability is determined by looking at the number of encirclements of the point (−1, 0). The range of gains over which the system will be stable can be determined by looking at crossings of the real axis.
The Nyquist plot can provide some information about the shape of the transfer function. For instance, the plot provides information on the difference between the number of zeros and poles of the transfer function by the angle at which the curve approaches the origin.
When drawn by hand, a cartoon version of the Nyquist plot is sometimes used, which shows the linearity of the curve, but where coordinates are distorted to show more detail in regions of interest. When plotted computationally, one needs to be careful to cover all frequencies of interest. This typically means that the parameter is swept logarithmically, in order to cover a wide range of values.
Background.
The mathematics uses the Laplace transform, which transforms integrals and derivatives in the time domain to simple multiplication and division in the "s" domain.
We consider a system whose transfer function is formula_1; when placed in a closed loop with negative feedback formula_2, the closed loop transfer function (CLTF) then becomes:
Stability can be determined by examining the roots of the desensitivity factor polynomial formula_4, e.g. using the Routh array, but this method is somewhat tedious. Conclusions can also be reached by examining the open loop transfer function (OLTF) formula_5, using its Bode plots or, as here, its polar plot using the Nyquist criterion, as follows.
Any Laplace domain transfer function formula_6 can be expressed as the ratio of two polynomials:
The roots of formula_8 are called the "zeros" of formula_6, and the roots of formula_10 are the "poles" of formula_6. The poles of formula_6 are also said to be the roots of the "characteristic equation" formula_13.
The stability of formula_6 is determined by the values of its poles: for stability, the real part of every pole must be negative. If formula_6 is formed by closing a negative unity feedback loop around the open-loop transfer function,
then the roots of the characteristic equation are also the zeros of formula_17, or simply the roots of formula_18.
Cauchy's argument principle.
From complex analysis, a contour formula_19 drawn in the complex formula_20 plane, encompassing but not passing through any number of zeros and poles of a function formula_21, can be mapped to another plane (named formula_21 plane) by the function formula_23. Precisely, each complex point formula_20 in the contour formula_19 is mapped to the point formula_21 in the new formula_21 plane yielding a new contour.
The Nyquist plot of formula_21, which is the contour formula_29 will encircle the point formula_30 of the formula_21 plane formula_32 times, where formula_33 by Cauchy's argument principle. Here formula_34 and formula_35 are, respectively, the number of zeros of formula_36 and poles of formula_21 inside the contour formula_19. Note that we count encirclements in the formula_21 plane in the same sense as the contour formula_19 and that encirclements in the opposite direction are "negative" encirclements. That is, we consider clockwise encirclements to be positive and counterclockwise encirclements to be negative.
Instead of Cauchy's argument principle, the original paper by Harry Nyquist in 1932 uses a less elegant approach. The approach explained here is similar to the approach used by Leroy MacColl (Fundamental theory of servomechanisms 1945) or by Hendrik Bode (Network analysis and feedback amplifier design 1945), both of whom also worked for Bell Laboratories. This approach appears in most modern textbooks on control theory.
Definition.
We first construct the Nyquist contour, a contour that encompasses the right-half of the complex plane:
The Nyquist contour mapped through the function formula_47 yields a plot of formula_47 in the complex plane. By the argument principle, the number of clockwise encirclements of the origin must be the number of zeros of formula_47 in the right-half complex plane minus the number of poles of formula_47 in the right-half complex plane. If instead, the contour is mapped through the open-loop transfer function formula_1, the result is the Nyquist Plot of formula_1. By counting the resulting contour's encirclements of −1, we find the difference between the number of poles and zeros in the right-half complex plane of formula_47. Recalling that the zeros of formula_47 are the poles of the closed-loop system, and noting that the poles of formula_47 are same as the poles of formula_1, we now state the Nyquist Criterion:"Given a Nyquist contour formula_19, let formula_35 be the number of poles of formula_1 encircled by formula_19, and formula_34 be the number of zeros of formula_47 encircled by formula_19. Alternatively, and more importantly, if formula_34 is the number of poles of the closed loop system in the right half plane, and formula_35 is the number of poles of the open-loop transfer function formula_1 in the right half plane, the resultant contour in the formula_1-plane, formula_68 shall encircle (clockwise) the point formula_69 formula_32 times such that formula_71."If the system is originally open-loop unstable, feedback is necessary to stabilize the system. Right-half-plane (RHP) poles represent that instability. For closed-loop stability of a system, the number of closed-loop roots in the right half of the "s"-plane must be zero. Hence, the number of counter-clockwise encirclements about formula_72 must be equal to the number of open-loop poles in the RHP. Any clockwise encirclements of the critical point by the open-loop frequency response (when judged from low frequency to high frequency) would indicate that the feedback control system would be destabilizing if the loop were closed. (Using RHP zeros to "cancel out" RHP poles does not remove the instability, but rather ensures that the system will remain unstable even in the presence of feedback, since the closed-loop roots travel between open-loop poles and zeros in the presence of feedback. In fact, the RHP zero can make the unstable pole unobservable and therefore not stabilizable through feedback.)
The Nyquist criterion for systems with poles on the imaginary axis.
The above consideration was conducted with an assumption that the open-loop transfer function formula_1 does not have any pole on the imaginary axis (i.e. poles of the form formula_74). This results from the requirement of the argument principle that the contour cannot pass through any pole of the mapping function. The most common case are systems with integrators (poles at zero).
To be able to analyze systems with poles on the imaginary axis, the Nyquist Contour can be modified to avoid passing through the point formula_74. One way to do it is to construct a semicircular arc with radius formula_76 around formula_74, that starts at formula_78 and travels anticlockwise to formula_79. Such a modification implies that the phasor formula_1 travels along an arc of infinite radius by formula_81, where formula_82 is the multiplicity of the pole on the imaginary axis.
Mathematical derivation.
Our goal is to, through this process, check for the stability of the transfer function of our unity feedback system with gain "k", which is given by
That is, we would like to check whether the characteristic equation of the above transfer function, given by
has zeros outside the open left-half-plane (commonly initialized as OLHP).
We suppose that we have a clockwise (i.e. negatively oriented) contour formula_19 enclosing the right half plane, with indentations as needed to avoid passing through zeros or poles of the function formula_1. Cauchy's argument principle states that
Where formula_34 denotes the number of zeros of formula_10 enclosed by the contour and formula_35 denotes the number of poles of formula_10 by the same contour. Rearranging, we have
formula_92, which is to say
We then note that formula_94 has exactly the same poles as formula_1. Thus, we may find formula_35 by counting the poles of formula_1 that appear within the contour, that is, within the open right half plane (ORHP).
We will now rearrange the above integral via substitution. That is, setting formula_98, we have
We then make a further substitution, setting formula_100. This gives us
We now note that formula_102 gives us the image of our contour under formula_1, which is to say our Nyquist plot. We may further reduce the integral
by applying Cauchy's integral formula. In fact, we find that the above integral corresponds precisely to the number of times the Nyquist plot encircles the point formula_105 clockwise. Thus, we may finally state that
We thus find that formula_107 as defined above corresponds to a stable unity-feedback system when formula_34, as evaluated above, is equal to 0.


Tebis

Tebis ("Technische Entwicklung Beratung und Individuelle Software") is a CAD/CAM software provided by Tebis AG, with headquarters in Martinsried near Munich/Germany.
Development locations: Martinsried and Norderstedt, Germany
International locations: China, Spain, France, Italy, Portugal, Sweden, United Kingdom, USA.
Functionality.
Tebis is a CAD/CAM software for industries such as die, mold or model manufacturing. The software is primarily to create toolpaths for machining operations such as drilling, milling and turning, but also for Wire EDM and sinker EDM. These toolpaths control multi-axis CNC machines. Other applications include manufacturing planning, design, reverse engineering, quality assurance, CNC machining and assembly. The software features interfaces for neutral file formats as well as proprietary formats of third-party manufacturers (STEP 203/214, VDAFS, IGES, DXF, STL, Parasolid, Catia V4/V5, Creo, SolidWorks, NX, JT, Inventor, Nastran, AutoForm).
Industrial application.
The programs are used in manufacturing companies of all sizes, from small and medium-sized companies to OEMs in the automotive and aerospace industries and their suppliers.
The following is a small sampling of companies who use the CAM system from Tebis.
The history of Tebis.
Tebis was founded in 1984. Following initial consulting jobs and business software projects, Tebis shifted its focus after six months to CAD/CAM. The first technical product was a PC-based station, which used a drawing board equipped with a position-measuring system to digitize transparent plans and convert them to scribed programs for milling machines.
Versions 1.0 to 1.0.4 constituted the first Tebis CAD/CAM system. As one of the first 3D systems, Tebis ran exclusively on PCs (DOS). Two monitors were required for its operation: One monitor displayed the real commands, while the other showed the geometries in 4 panels. The input commands were entered using a digitizer tablet. The milling programs were calculated only for individual surfaces. Because of the small RAM (256 bytes) in the NC machines of the 1980s, Tebis provided a DNC connection to enable postprocessing via a V24 line next to the NC machine.
The Tebis Version 2.0 with a graphical user interface was introduced in 1989. It is still used today in a much more advanced form, and is distinct from common Windows interfaces. This version made it possible to animate geometries onscreen in real-time. Tebis Automill technology, which allows users to calculate milling paths across surfaces, was introduced in Version 2.1.
Tebis Version 3.0 was presented in 1993. The system was modularized and expanded for operation under the SCO UNIX, HP-UX, IRIX and AIX operating systems. Version 3.1 included the Milling Wizard, version V3.2 featured interactive CAD and version V3.3 offered the first integration of a tool library and parameterized administration for all NC calculations. In Version 3.4, modules for the simulation of machining at a virtual CNC machine the design of electrodes for EDM, and 2.5D milling and drilling were added. Starting with Version 3.5, variable machining templates can be used for even better NC programming automation. For the first time this version also included the Job Manager as a central control element for all machining steps. The CAD module for BREP design was integrated in the software, enabling Tebis to be used for the entire manufacturing process in die, mold and model manufacturing. Version 4.0 was provided with a new user interface specifically designed for CAD/CAM applications and a new platform for 2.5D and 3D feature-based NC automation. For the first time, this version supported CNC lathes and industrial robots, and the manufacturing technologies of laser hardening and laser weld cladding.
The current Tebis Version 4.1 was launched in 2020 with an internally-developed parametric-associative CAD system base. The hybrid CAD system combines free-form surfaces, solids and digitized data and provides Tebis template technology also in the CAD environment. Parametric CAD templates automate design and CAD manufacturing preparation. The user interface has also been optimized in terms of simplicity and automation for CAM users.
Tebis is one of the global market leaders in CAM software. The owner-managed company also has its own consulting unit working with companies primarily in die, mold and model manufacturing. Services include industry-specific process and management consulting and optimizing the processes of these companies.
After acquiring a division of ID Ingenieurgesellschaft für Datentechnik mbH, Tebis now also offers a manufacturing execution system (MES) called ProLeiS that can be integrated in the CAD/CAM application.


RigExpert

Rig Expert Ukraine Ltd is a manufacturer of ham and PMR Two-way radio RF antenna analysis and antenna tuning equipment. The company was founded in 2003 and is headquartered in Kyiv, Ukraine.
Current products.
The AA-30, AA-54 & AA-170 are almost the same product except for the frequency range. Similarly, the AA-600, AA-1000 & AA-1400 are the same product except for the different frequency range.


Proximal gradient method

Proximal gradient methods are a generalized form of projection used to solve non-differentiable convex optimization problems.
Many interesting problems can be formulated as convex optimization problems of the form
formula_1
where formula_2 are possibly non-differentiable convex functions. The lack of differentiability rules out conventional smooth optimization techniques like the steepest descent method and the conjugate gradient method, but proximal gradient methods can be used instead.
Proximal gradient methods starts by a splitting step, in which the functions formula_3 are used individually so as to yield an easily implementable algorithm. They are called proximal because each non-differentiable function among formula_3 is involved via its proximity operator. Iterative shrinkage thresholding algorithm, projected Landweber, projected gradient, alternating projections, alternating-direction method of multipliers, alternating
split Bregman are special instances of proximal algorithms.
For the theory of proximal gradient methods from the perspective of and with applications to statistical learning theory, see proximal gradient methods for learning.
Projection onto convex sets (POCS).
One of the widely used convex optimization algorithms is projections onto convex sets (POCS). This algorithm is employed to recover/synthesize a signal satisfying simultaneously several convex constraints. Let formula_5 be the indicator function of non-empty closed convex set formula_6 modeling a constraint. This reduces to convex feasibility problem, which require us to find a solution such that it lies in the intersection of all convex sets formula_6. In POCS method each set formula_6 is incorporated by its projection operator formula_9. So in each iteration formula_10 is updated as
However beyond such problems projection operators are not appropriate and more general operators are required to tackle them. Among the various generalizations of the notion of a convex projection operator that exist, proximity operators are best suited for other purposes.
Examples.
Special instances of Proximal Gradient Methods are


Tegra Note 7

The Tegra Note 7 is a mini tablet computer and the second Tegra 4 based mobile device designed by Nvidia that runs the Android operating system.
Release.
Revealed on September 18, 2013, EVGA was the first to partner with Nvidia for release on November 19, 2013. Other manufacturers Nvidia has partnered with include Advent, ZOTAC, PNY, Gigabyte, Xolo HP and Cherry Mobile.
The device is known as EVGA Tegra Note 7 in the US, Advent Vega Tegra Note 7 in the United Kingdom, Gradiente Tegra Note 7 in Brazil, Gazer Tegra Note 7 in Ukraine and Russia, Gigabyte Tegra Note 7 in Australia and New Zealand, Cherry Mobile Tegra Note 7 in the Philippines and XOLO PLAY Tegra Note 7 in India. HP has rebranded the Tegra Note 7 as the HP Slate 7 Extreme.
Features.
The Note 7 uses a 1.8 GHz quad-core Tegra 4 chipset with 1 GB of RAM; Nvidia claims that the chipset and other improvements make it the fastest 7-inch tablet on the market offering 50% faster browsing experience than tablets twice the price. Notable features of the device include enhanced capacitive "DirectStylus" technology that is three times more responsive, premium Tegra 4 audio processing with PureAudio, and world's first HDR camera in a tablet with Nvidia Chimera computational photography. The 1280×800 display use Nvidia PRISM 2 display processing, which modulates the display backlight and per-pixel color values to extend battery life 40% for up to 10 hours of HD video playback.
Software updates.
Nvidia released Tegra Note 7 System Update 3.0 (Android 5.1) on July 23, 2015.


Proximal gradient methods for learning

Proximal gradient (forward backward splitting) methods for learning is an area of research in optimization and statistical learning theory which studies algorithms for a general class of convex regularization problems where the regularization penalty may not be differentiable. One such example is formula_1 regularization (also known as Lasso) of the form
Proximal gradient methods offer a general framework for solving regularization problems from statistical learning theory with penalties that are tailored to a specific problem application. Such customized penalties can help to induce certain structure in problem solutions, such as "sparsity" (in the case of lasso) or "group structure" (in the case of group lasso).
Relevant background.
Proximal gradient methods are applicable in a wide variety of scenarios for solving convex optimization problems of the form
where formula_4 is convex and differentiable with Lipschitz continuous gradient, formula_5 is a convex, lower semicontinuous function which is possibly nondifferentiable, and formula_6 is some set, typically a Hilbert space. The usual criterion of formula_7 minimizes formula_8 if and only if formula_9 in the convex, differentiable setting is now replaced by
where formula_11 denotes the subdifferential of a real-valued, convex function formula_12.
Given a convex function formula_13 an important operator to consider is its proximal operator formula_14 defined by
which is well-defined because of the strict convexity of the formula_16 norm. The proximal operator can be seen as a generalization of a projection.
We see that the proximity operator is important because formula_17 is a minimizer to the problem formula_18 if and only if
Moreau decomposition.
One important technique related to proximal gradient methods is the Moreau decomposition, which decomposes the identity operator as the sum of two proximity operators. Namely, let formula_21 be a lower semicontinuous, convex function on a vector space formula_22. We define its Fenchel conjugate formula_23 to be the function
The general form of Moreau's decomposition states that for any formula_25 and any formula_20 that
which for formula_28 implies that formula_29. The Moreau decomposition can be seen to be a generalization of the usual orthogonal decomposition of a vector space, analogous with the fact that proximity operators are generalizations of projections.
In certain situations it may be easier to compute the proximity operator for the conjugate formula_30 instead of the function formula_31, and therefore the Moreau decomposition can be applied. This is the case for group lasso.
Lasso regularization.
Consider the regularized empirical risk minimization problem with square loss and with the formula_1 norm as the regularization penalty:
where formula_34 The formula_1 regularization problem is sometimes referred to as "lasso" (least absolute shrinkage and selection operator). Such formula_1 regularization problems are interesting because they induce " sparse" solutions, that is, solutions formula_37 to the minimization problem have relatively few nonzero components. Lasso can be seen to be a convex relaxation of the non-convex problem
where formula_39 denotes the formula_40 "norm", which is the number of nonzero entries of the vector formula_37. Sparse solutions are of particular interest in learning theory for interpretability of results: a sparse solution can identify a small number of important factors.
Solving for L1 proximity operator.
For simplicity we restrict our attention to the problem where formula_42. To solve the problem
we consider our objective function in two parts: a convex, differentiable term formula_44 and a convex function formula_45. Note that formula_46 is not strictly convex.
Let us compute the proximity operator for formula_47. First we find an alternative characterization of the proximity operator formula_48 as follows:
formula_49
For formula_45 it is easy to compute formula_51: the formula_52th entry of formula_51 is precisely
Using the recharacterization of the proximity operator given above, for the choice of formula_45 and formula_20 we have that formula_57 is defined entrywise by
which is known as the soft thresholding operator formula_59.
Fixed point iterative schemes.
To finally solve the lasso problem we consider the fixed point equation shown earlier:
Given that we have computed the form of the proximity operator explicitly, then we can define a standard fixed point iteration procedure. Namely, fix some initial formula_61, and for formula_62 define
Note here the effective trade-off between the empirical error term formula_64 and the regularization penalty formula_47. This fixed point method has decoupled the effect of the two different convex functions which comprise the objective function into a gradient descent step (formula_66) and a soft thresholding step (via formula_67).
Convergence of this fixed point scheme is well-studied in the literature and is guaranteed under appropriate choice of step size formula_68 and loss function (such as the square loss taken here). Accelerated methods were introduced by Nesterov in 1983 which improve the rate of convergence under certain regularity assumptions on formula_4. Such methods have been studied extensively in previous years.
For more general learning problems where the proximity operator cannot be computed explicitly for some regularization term formula_46, such fixed point schemes can still be carried out using approximations to both the gradient and the proximity operator.
Practical considerations.
There have been numerous developments within the past decade in convex optimization techniques which have influenced the application of proximal gradient methods in statistical learning theory. Here we survey a few important topics which can greatly improve practical algorithmic performance of these methods.
Adaptive step size.
In the fixed point iteration scheme
one can allow variable step size formula_72 instead of a constant formula_68. Numerous adaptive step size schemes have been proposed throughout the literature. Applications of these schemes suggest that these can offer substantial improvement in number of iterations required for fixed point convergence.
Elastic net (mixed norm regularization).
Elastic net regularization offers an alternative to pure formula_1 regularization. The problem of lasso (formula_1) regularization involves the penalty term formula_45, which is not strictly convex. Hence, solutions to formula_77 where formula_4 is some empirical loss function, need not be unique. This is often avoided by the inclusion of an additional strictly convex term, such as an formula_79 norm regularization penalty. For example, one can consider the problem
where formula_34
For formula_82 the penalty term formula_83 is now strictly convex, and hence the minimization problem now admits a unique solution. It has been observed that for sufficiently small formula_84, the additional penalty term formula_85 acts as a preconditioner and can substantially improve convergence while not adversely affecting the sparsity of solutions.
Exploiting group structure.
Proximal gradient methods provide a general framework which is applicable to a wide variety of problems in statistical learning theory. Certain problems in learning can often involve data which has additional structure that is known " a priori". In the past several years there have been new developments which incorporate information about group structure to provide methods which are tailored to different applications. Here we survey a few such methods.
Group lasso.
Group lasso is a generalization of the lasso method when features are grouped into disjoint blocks. Suppose the features are grouped into blocks formula_86. Here we take as a regularization penalty
which is the sum of the formula_79 norm on corresponding feature vectors for the different groups. A similar proximity operator analysis as above can be used to compute the proximity operator for this penalty. Where the lasso penalty has a proximity operator which is soft thresholding on each individual component, the proximity operator for the group lasso is soft thresholding on each group. For the group formula_89 we have that proximity operator of formula_90 is given by
where formula_89 is the formula_93th group.
In contrast to lasso, the derivation of the proximity operator for group lasso relies on the Moreau decomposition. Here the proximity operator of the conjugate of the group lasso penalty becomes a projection onto the ball of a dual norm.
Other group structures.
In contrast to the group lasso problem, where features are grouped into disjoint blocks, it may be the case that grouped features are overlapping or have a nested structure. Such generalizations of group lasso have been considered in a variety of contexts. For overlapping groups one common approach is known as "latent group lasso" which introduces latent variables to account for overlap. Nested group structures are studied in "hierarchical structure prediction" and with directed acyclic graphs.


MOSFET Gate Driver

MOSFET gate driver is a specialized circuit that is used to drive the gate (gate driver) of power MOSFETs effectively and efficiently in high-speed switching applications. The addition of high-speed MOSFET gate drivers are the last step if the turn-on is intended to fully enhance the conducting channel of the MOSFET technology.
MOSFET technology.
The gate driver works under the same principle as the MOSFET transistor. It provides an output current that provides a charge to the semiconductor by a control electrode. It is also simple to drive and has resistive nature for power uses.


Occam learning

In computational learning theory, Occam learning is a model of algorithmic learning where the objective of the learner is to output a succinct representation of received training data. This is closely related to probably approximately correct (PAC) learning, where the learner is evaluated on its predictive power of a test set.
Occam learnability implies PAC learning, and for a wide variety of concept classes, the converse is also true: PAC learnability implies Occam learnability.
Introduction.
Occam Learning is named after Occam's razor, which is a principle stating that, given all other things being equal, a shorter explanation for observed data should be favored over a lengthier explanation. The theory of Occam learning is a formal and mathematical justification for this principle. It was first shown by Blumer, et al. that Occam learning implies PAC learning, which is the standard model of learning in computational learning theory. In other words, "parsimony" (of the output hypothesis) implies "predictive power".
Definition of Occam learning.
The succinctness of a concept formula_1 in concept class formula_2 can be expressed by the length formula_3 of the shortest bit string that can represent formula_1 in formula_2. Occam learning connects the succinctness of a learning algorithm's output to its predictive power on unseen data.
Let formula_2 and formula_7 be concept classes containing target concepts and hypotheses respectively. Then, for constants formula_8 and formula_9, a learning algorithm formula_10 is an formula_11-Occam algorithm for formula_2 using formula_7 iff, given a set formula_14 of formula_15 samples labeled according to a concept formula_16, formula_10 outputs a hypothesis formula_18 such that
where formula_24 is the maximum length of any sample formula_25. An Occam algorithm is called "efficient" if it runs in time polynomial in formula_24, formula_15, and formula_28 We say a concept class formula_2 is "Occam learnable" with respect to a hypothesis class formula_7 if there exists an efficient Occam algorithm for formula_2 using formula_32
The relation between Occam and PAC learning.
Occam learnability implies PAC learnability, as the following theorem of Blumer, et al. shows:
Theorem ("Occam learning implies PAC learning").
Let formula_10 be an efficient formula_11-Occam algorithm for formula_2 using formula_7. Then there exists a constant formula_37 such that for any formula_38, for any distribution formula_39, given formula_40 samples drawn from formula_39 and labelled according to a concept formula_42 of length formula_24 bits each, the algorithm formula_10 will output a hypothesis formula_45 such that formula_46 with probability at least formula_47 .Here, formula_48 is with respect to the concept formula_1 and distribution formula_39. This implies that the algorithm formula_10 is also a PAC learner for the concept class formula_2 using hypothesis class formula_7. A slightly more general formulation is as follows:
Theorem ("Occam learning implies PAC learning, cardinality version").
Let formula_38. Let formula_10 be an algorithm such that, given formula_15 samples drawn from a fixed but unknown distribution formula_57 and labeled according to a concept formula_42 of length formula_24 bits each, outputs a hypothesis formula_60 that is consistent with the labeled samples. Then, there exists a constant formula_61 such that if formula_62, then formula_10 is guaranteed to output a hypothesis formula_60 such that formula_46 with probability at least formula_47.
While the above theorems show that Occam learning is sufficient for PAC learning, it doesn't say anything about "necessity." Board and Pitt show that, for a wide variety of concept classes, Occam learning is in fact necessary for PAC learning. They proved that for any concept class that is "polynomially closed under exception lists," PAC learnability implies the existence of an Occam algorithm for that concept class. Concept classes that are polynomially closed under exception lists include Boolean formulas, circuits, deterministic finite automata, decision-lists, decision-trees, and other geometrically-defined concept classes.
A concept class formula_2 is polynomially closed under exception lists if there exists a polynomial-time algorithm formula_68 such that, when given the representation of a concept formula_42 and a finite list formula_70 of "exceptions", outputs a representation of a concept formula_71 such that the concepts formula_1 and formula_73 agree except on the set formula_70.
Proof that Occam learning implies PAC learning.
We first prove the Cardinality version. Call a hypothesis formula_75 "bad" if formula_76, where again formula_48 is with respect to the true concept formula_1 and the underlying distribution formula_57. The probability that a set of samples formula_21 is consistent with formula_19 is at most formula_82, by the independence of the samples. By the union bound, the probability that there exists a bad hypothesis in formula_83 is at most formula_84, which is less than formula_85 if formula_86. This concludes the proof of the second theorem above.
Using the second theorem, we can prove the first theorem. Since we have a formula_11-Occam algorithm, this means that any hypothesis output by formula_10 can be represented by at most formula_89 bits, and thus formula_90. This is less than formula_91 if we set formula_92 for some constant formula_37. Thus, by the Cardinality version Theorem, formula_10 will output a consistent hypothesis formula_19 with probability at least formula_96. This concludes the proof of the first theorem above.
Improving sample complexity for common problems.
Though Occam and PAC learnability are equivalent, the Occam framework can be used to produce tighter bounds on the sample complexity of classical problems including conjunctions, conjunctions with few relevant variables, and decision lists.
Extensions.
Occam algorithms have also been shown to be successful for PAC learning in the presence of errors, probabilistic concepts, function learning and Markovian non-independent examples.


SIM.JS

SIM.JS is an event-based discrete-event simulation library based on standard
JavaScript. The library has been written in order to enable simulation within standard browsers by utilizing web technology.
SIM.JS supports entities, resources (Facility, Buffers and Stores), communication (via Timers, Events and Messages) and statistics
(with Data Series, Time Series and Population statistics).
The SIM.JS distribution contains tutorials, in-depth documentation, and a large
number of examples.
SIM.JS is released as open source software under the LGPL license. The first version was released in January 2011.
Example.
There are several examples bundled with the library download. Trafficlight simulation is a standard simulation problem, which may be simulated as within this example:


GoIP

GoIP is a GSM-gateway[1] and SIM bank produced by the Hybertone and DBL technology companies. It enables connections between the GSM network and VoIP.
Usage concept.
Sim-card is put into GSM-gateways (or SIM-bank connected to GSM-gateway) in order to register it with the GSM network, at the same time the gateway is associated with VoIP through program switch. Accordingly, the traffic can be converted in and out between GSM and VoIP channels. SIP and H.323 protocols are used for media traffic termination. GoIP equipment is compatible with all main IP PBX: Asterisk, Mera, Oktell, 3CX, etc.
Compared with PSTN, GSM-gateways provide a drastic economy by amending the infrastructure and lowering the expenditures on technical support.
GoIP includes integral support of SIP and H.323 protocols with flexible settings. Duplex authentification of password and trust-list backup will significantly decrease telecommunication expenditures while maintaining an adaptable system of call transfer. The GoIP gateway supports several devices' groups, with flexible settings of large GSM-gateways groups with different channels.
There are several models of GoIP GSM gateways.
Applications of GoIP gateways: They are vastly usable by system integrators, TCP, call centers, large and little companies, and domestic users of VoIP as well.
VoIP-GSM gateways produced on the GoIP platform help to accomplish the following:
Adding the mobile lines in the existing telephone system (GoIP provides a GSM network between telephone systems and IP PBX, and ensures a fast connection to PSTN where usual telephone lines are unavailable)
Organization of outbound call-centers
Call transfer from GSM into SIP and backward (inbound and outbound calls between GSM and VoIP)
Determination of SIM-bank.
SIM-bank is a SIM-card controller that provides remote control over VoIP GSM gateways and allows to simplify and automatize many procedures likewise:
- fast connection of SIM cards to the gateway, rapid exchange of SIM-cards via the Internet, and their prearranged synchronous replacement.
The cooperative use of GoIP gateways and GoIP SIM-bank enables the management of unmanned devices and reduces the work pressure in SIM-cards operations, for example, SIM-cards replacement and replenishment.
The remote access advantages for SIM cards.
Central management of SIM cards,
their dynamic allocation,
no need to change or reinsert the SIM card in the device,
rapid replacement of SIM cards with no breakdowns in service.
For instance, the remote GoIP gateway will no longer require the replacement of SIM cards in the device or their reinsertion. One can manage the group of GoIP gateways remotely, effectively, and with the minimal loss with the help of a SIM bank. The main advantages of SIM-bank appliances include 1) the replacement of SIM cards in gateways channels that are territorially remote from the very SIM bank and other gateways in order to transfer the SIM cards between the base stations of GSM operator and 2) autonomous work that supports from 32 to 128 channels for SIM-cards independent connections.
Sources:


Homomorphic secret sharing

In cryptography, homomorphic secret sharing is a type of secret sharing algorithm in which the secret is encrypted via homomorphic encryption. A homomorphism is a transformation from one algebraic structure into another of the same type so that the structure is preserved. Importantly, this means that for every kind of manipulation of the original data, there is a corresponding manipulation of the transformed data.
Technique.
Homomorphic secret sharing is used to transmit a secret to several recipients as follows:
Examples.
Suppose a community wants to perform an election, using a decentralized voting protocol, but they want to ensure that the vote-counters won't lie about the results. Using a type of homomorphic secret sharing known as Shamir's secret sharing, each member of the community can add their vote to a form that is split into pieces, each piece is then submitted to a different vote-counter. The pieces are designed so that the vote-counters can't predict how any alterations to each piece will affect the whole, thus, discouraging vote-counters from tampering with their pieces. When all votes have been received, the vote-counters combine them, allowing them to recover the aggregate election results.
In detail, suppose we have an election with:
Features.
This protocol works as long as not all of the "k" authorities are corrupt — if they were, then they could collaborate to reconstruct "P"("x") for each voter and also subsequently alter the votes.
The protocol requires authorities to be completed, therefore in case there are authorities, authorities can be corrupted, which gives the protocol a certain degree of robustness.
The protocol manages the IDs of the voters (the IDs were submitted with the ballots) and therefore can verify that only legitimate voters have voted.
Under the assumptions on "t":
The protocol implicitly prevents corruption of ballots.
This is because the authorities have no incentive to change the ballot since each authority has only a share of the ballot and has no knowledge how changing this share will affect the outcome.


SecureLog

In cryptology, SecureLog is an algorithm used to convert digital data into trusted data that can be verified if the authenticity is questioned. SecureLog is used in IT solutions that generates data to support compliance regulations like SOX.
History.
An algorithm used to make datalogs secure from manipulation. The first infrastructure supporting the algorithm was available on the Internet in 2006.
Operation.
SecureLog involves an "active key provider", a "managed data store" and a "verification provider".
Uses.
The algorithm is used in several different use cases:


NETDATA

NETDATA is a file format used primarily for data transfer and storage on IBM mainframe systems, although implementations are available for other systems.
Description.
NETDATA files are 80-byte card image files containing unloaded file data plus metadata to allow the original file to be reconstituted on the receiving system. A complete NETDATA file consists of a number of "control records", followed by "data records" and terminated by a "trailer record". All records have the same format:
Control records.
Control records have a six-character EBCDIC identifier in bytes 2-7 following the length and flags. They contain a number of self-defining fields, called "text units". Each text unit consists of a two byte "text unit key" identifying this text unit, a two-byte big-endian binary number of length-data pairs that follow for this key (usually one), a two byte length field identifying the length of the text unit data, and a text unit of the specified length. Implementations are expected to ignore any text unit information not relevant to the receiving system.
Header Control Record
The header record must be the first record of a NETDATA file. It has the identifier "INMR01". It contains information identifying the sender: node (host), timestamp, and user id, the length of the control record segments, and the target (receiving) node and user id. It may optionally contain a request for acknowledgement of receipt, the version number of the data format, the number of files in the transmission, and a "user parameter string." CMS allows only one file per transmission, but TSO/E and other systems may allow more than one.
File Utility Control Record
This record describes how the file's data is to be reconstituted. Its identifier is "INMR02". Bytes 8-11 contain the big-endian binary number of the file to which this record applies. If there are multiple files in a transmission they are numbered starting with one. The rest of this record describes the file's format, and one or more steps ("utility programs") which must be executed in order to rebuild this file. The text units identify the file's organization (INMDSORG: sequential, partitioned, etc.), its fixed of maximum record length (INMLRECL), its record format (INMRECFM: fixed, variable, etc) the approximate size of the file (IBMSIZE), and the utility program name(s) (INMUTILN). It may also contain the file's block size, creation date, number of directory blocks, name, expiration date, file mode number, last change date, last reference date, member name list (for partitioned datasets), a note file, and a user parameter string.
Data Control Record
The Data Control Record immediately precedes the data and describes its format, similar to the Utility Control Record. Its identifier is "INMR03". This record is ignored by CMS, but is used by TSO/E. It contains the file's organization (INMDSORG), its record length (INMLRECL), its record format (INMRECFM), and the file size (IBMSIZE).
User Control Record
The User Control record can appear at any point in the data stream. Its identifier is "INMR04". If present it is ignored by CMS, but may be used by other systems. It contains only a User Parameter String (INMUSERP).
Trailer Control Record
This record marks the end of the file. Its identifier is "INMR06". No other data is defined for this record.
Acknowledgement Control Record
This record has an id of "INMR07". It is used by the receiving system to acknowledge receipt of a transmission. It contains one of the text units File Name (INMDSNM) or Note File (INMTERM) plus, optionally, the Origin Time Stamp (INMFTIME).
A note file (sometimes called a "PROFS note") "is a short communication, the kind usually done by letter.".
Data records.
Data records (identified by their flag value), follow the Data Control Record, if present, and precede the Trailer Control Record. Records can be any size up to INMLRECL. They are sent as multiple segments of up to 253 bytes, split into 80 byte records for transmission, and reassembled by the receiver. Settings of the flags byte in each record mark the beginning, end, or a complete record of the file. Bytes of a record can contain any bit pattern. No character values are reserved.


CNC machine tool monitoring by AE sensors

A machine tool monitoring system is a flow of information and system processing in which the information selection, obtaining data, processing of information and decision making on the refined information are integrated. The aim of tool condition monitoring is to detect early the disturbances in the machining process and wear of machine tool components.
The condition of tool has been researched extensively in the past and have focused on detection of tool wear, tool breakage and the estimation of remaining tool life. It is very important for on-line identification of tool condition in machining process for enhanced productivity, better quality of parts and lower costs for unmanned, automated manufacturing systems.
Techniques of machine tool monitoring.
Machine tool monitoring can be done with or without additional sensors. Using additional sensors, monitoring can be done by measuring:
Sensor-less machine tool monitoring is done by measuring internal drive signals such as:
Combined measuring of multiple quantities is also possible.
Acoustic emission sensor.
Machine tool monitoring is explained with Acoustic Emission (AE) sensors. An AE sensor is commonly defined as the sound emitted as an elastic wave by a solid when it is deformed or struck, caused by the rapid release of localized stress energy. Therefore, it is an occurrence phenomenon which releases elastic energy into the material, which then propagates as an elastic wave. The detection frequency range of acoustic emission is from 1 kHz to 1 MHz.
Rapid stress-releasing events generate a spectrum of stress waves starting at 0 Hz and typically falling off at several MHz. AE can be related to an irreversible release of energy. It can also be generated from sources not involving material failure including friction, cavitation and impact. The three major applications of AE sensors phenomena are: a) Source location - determine the locations of occurrence of an event b) Material mechanical performance - evaluate and characterize materials/structures; and c Health monitoring – monitors the safety operation.
How an AE sensor monitors machine tool.
An AE sensor works on the principle of measuring the high-frequency energy signals produced during cutting process. It also measures the AE energy resulting from the fracture when a tool breaks. It is best suited to applications where the level of background AE signal is low compared to the sound of tool breakage. This makes the AE sensor ideal for breakage detection of small drills and taps. It is easy to install on both new and existing machines.
An AE sensor detects force proportional monitoring signals even in machining operations, which generate very small cutting forces. In combination with true power, it increases the reliability of breakage monitoring. It is used especially with solid carbide tools, or very small tools on large machines and multi spindles. Most of the sensors have to be attached to the machine tool surface. However, there are alternative methods of AE wave transmitting. A rotating, wireless AE sensor consists of a rotating sensor and a fixed receiver. An AE sensor can also receive the acoustic waves via a jet of cooling lubricant, which can be connected directly to the tool or workpiece.
The machine tool monitoring systems commonly use sensors for measuring cutting force components or quantities related to cutting force (power, torque, distance/displacement and strain). AE sensors are relatively easy to install in existing or new machines, and do not influence machine integrity and stiffness. All systems suppliers also use acoustic emission sensors, especially for monitoring small tools and for grinding.
All sensors used in machine tool monitoring systems are well adjusted to harsh machine tool environments. The difficulties in designing reliable machine tool monitoring can be related to the complexity of the machining process itself, which may have one or more of the following characteristics, apart from the changes of the machine tool itself.


Integral windup

Integral windup, also known as integrator windup or reset windup, refers to the situation in a PID controller where a large change in setpoint occurs (say a positive change) and the integral term accumulates a significant error during the rise (windup), thus overshooting and continuing to increase as this accumulated error is unwound (offset by errors in the other direction). The specific problem is the excess overshooting.
Solutions.
This problem can be addressed by
Occurrence.
Integral windup particularly occurs as a limitation of physical systems, compared with ideal systems, due to the ideal output being physically impossible (process : the output of the process being limited at the top or bottom of its scale, making the error constant). For example, the position of a valve cannot be any more open than fully open and also cannot be closed any more than fully closed. In this case, anti-windup can actually involve the integrator being turned off for periods of time until the response falls back into an acceptable range.
This usually occurs when the controller's output can no longer affect the controlled variable, or if the controller is part of a selection scheme and it is selected right.
Integral windup was more of a problem in analog controllers. Within modern distributed control systems and programmable logic controllers, it is much easier to prevent integral windup by either limiting the controller output, limiting the integral to produce feasible output, or by using external reset feedback, which is a means of feeding back the selected output to the integral circuit of all controllers in the selection scheme so that a closed loop is maintained.


Admission control

Admission control is a validation process in communication systems where a check is performed before a connection is established to see if current resources are sufficient for the proposed connection.
Applications.
For some applications, dedicated resources (such as a wavelength across an optical network) may be needed in which case admission control has to verify availability of such resources before a request can be admitted.
For more elastic applications, a total volume of resources may be needed prior to some deadline in order to satisfy a new request, in which case admission control needs to verify availability of resources at the time and perform scheduling to guarantee satisfaction of an admitted request.


Model predictive control

Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The main advantage of MPC is the fact that it allows the current timeslot to be optimized, while keeping future timeslots in account. This is achieved by optimizing a finite time-horizon, but only implementing the current timeslot and then optimizing again, repeatedly, thus differing from a linear–quadratic regulator (LQR). Also MPC has the ability to anticipate future events and can take control actions accordingly. PID controllers do not have this predictive ability. MPC is nearly universally implemented as a digital control, although there is research into achieving faster response times with specially designed analog circuitry.
Generalized predictive control (GPC) and dynamic matrix control (DMC) are classical examples of MPC.
Overview.
The models used in MPC are generally intended to represent the behavior of complex and simple dynamical systems. The additional complexity of the MPC control algorithm is not generally needed to provide adequate control of simple systems, which are often controlled well by generic PID controllers. Common dynamic characteristics that are difficult for PID controllers include large time delays and high-order dynamics.
MPC models predict the change in the dependent variables of the modeled system that will be caused by changes in the independent variables. In a chemical process, independent variables that can be adjusted by the controller are often either the setpoints of regulatory PID controllers (pressure, flow, temperature, etc.) or the final control element (valves, dampers, etc.). Independent variables that cannot be adjusted by the controller are used as disturbances. Dependent variables in these processes are other measurements that represent either control objectives or process constraints.
MPC uses the current plant measurements, the current dynamic state of the process, the MPC models, and the process variable targets and limits to calculate future changes in the dependent variables. These changes are calculated to hold the dependent variables close to target while honoring constraints on both independent and dependent variables. The MPC typically sends out only the first change in each independent variable to be implemented, and repeats the calculation when the next change is required.
While many real processes are not linear, they can often be considered to be approximately linear over a small operating range. Linear MPC approaches are used in the majority of applications with the feedback mechanism of the MPC compensating for prediction errors due to structural mismatch between the model and the process. In model predictive controllers that consist only of linear models, the superposition principle of linear algebra enables the effect of changes in multiple independent variables to be added together to predict the response of the dependent variables. This simplifies the control problem to a series of direct matrix algebra calculations that are fast and robust.
When linear models are not sufficiently accurate to represent the real process nonlinearities, several approaches can be used. In some cases, the process variables can be transformed before and/or after the linear MPC model to reduce the nonlinearity. The process can be controlled with nonlinear MPC that uses a nonlinear model directly in the control application. The nonlinear model may be in the form of an empirical data fit (e.g. artificial neural networks) or a high-fidelity dynamic model based on fundamental mass and energy balances. The nonlinear model may be linearized to derive a Kalman filter or specify a model for linear MPC.
An algorithmic study by El-Gherwi, Budman, and El Kamel shows that utilizing a dual-mode approach can provide significant reduction in online computations while maintaining comparative performance to a non-altered implementation. The proposed algorithm solves N convex optimization problems in parallel based on exchange of information among controllers.
Theory behind MPC.
 MPC is based on iterative, finite-horizon optimization of a plant model. At time formula_1 the current plant state is sampled and a cost minimizing control strategy is computed (via a numerical minimization algorithm) for a relatively short time horizon in the future: formula_2. Specifically, an online or on-the-fly calculation is used to explore state trajectories that emanate from the current state and find (via the solution of Euler–Lagrange equations) a cost-minimizing control strategy until time formula_3. Only the first step of the control strategy is implemented, then the plant state is sampled again and the calculations are repeated starting from the new current state, yielding a new control and new predicted state path. The prediction horizon keeps being shifted forward and for this reason MPC is also called receding horizon control. Although this approach is not optimal, in practice it has given very good results. Much academic research has been done to find fast methods of solution of Euler–Lagrange type equations, to understand the global stability properties of MPC's local optimization, and in general to improve the MPC method.
Principles of MPC.
Model predictive control is a multivariable control algorithm that uses:
An example of a quadratic cost function for optimization is given by:
without violating constraints (low/high limits) with
etc.
Nonlinear MPC.
Nonlinear model predictive control, or NMPC, is a variant of model predictive control that is characterized by the use of nonlinear system models in the prediction. As in linear MPC, NMPC requires the iterative solution of optimal control problems on a finite prediction horizon. While these problems are convex in linear MPC, in nonlinear MPC they are not necessarily convex anymore. This poses challenges for both NMPC stability theory and numerical solution.
The numerical solution of the NMPC optimal control problems is typically based on direct optimal control methods using Newton-type optimization schemes, in one of the variants: direct single shooting, direct multiple shooting methods, or direct collocation. NMPC algorithms typically exploit the fact that consecutive optimal control problems are similar to each other. This allows to initialize the Newton-type solution procedure efficiently by a suitably shifted guess from the previously computed optimal solution, saving considerable amounts of computation time. The similarity of subsequent problems is even further exploited by path following algorithms (or "real-time iterations") that never attempt to iterate any optimization problem to convergence, but instead only take a few iterations towards the solution of the most current NMPC problem, before proceeding to the next one, which is suitably initialized; see, e.g... Another promising candidate for the nonlinear optimization problem is to use a randomized optimization method. Optimum solutions are found by generating random samples that satisfy the constraints in the solution space and finding the optimum one based on cost function.
While NMPC applications have in the past been mostly used in the process and chemical industries with comparatively slow sampling rates, NMPC is being increasingly applied, with advancements in controller hardware and computational algorithms, e.g., preconditioning, to applications with high sampling rates, e.g., in the automotive industry, or even when the states are distributed in space (Distributed parameter systems). As an application in aerospace, recently, NMPC has been used to track optimal terrain-following/avoidance trajectories in real-time.
Explicit MPC.
Explicit MPC (eMPC) allows fast evaluation of the control law for some systems, in stark contrast to the online MPC. Explicit MPC is based on the parametric programming technique, where the solution to the MPC control problem formulated as optimization problem is pre-computed offline. This offline solution, i.e., the control law, is often in the form of a piecewise affine function (PWA), hence the eMPC controller stores the coefficients of the PWA for each a subset (control region) of the state space, where the PWA is constant, as well as coefficients of some parametric representations of all the regions. Every region turns out to geometrically be a convex polytope for linear MPC, commonly parameterized by coefficients for its faces, requiring quantization accuracy analysis. Obtaining the optimal control action is then reduced to first determining the region containing the current state and second a mere evaluation of PWA using the PWA coefficients stored for all regions. If the total number of the regions is small, the implementation of the eMPC does not require significant computational resources (compared to the online MPC) and is uniquely suited to control systems with fast dynamics. A serious drawback of eMPC is exponential growth of the total number of the control regions with respect to some key parameters of the controlled system, e.g., the number of states, thus dramatically increasing controller memory requirements and making the first step of PWA evaluation, i.e. searching for the current control region, computationally expensive.
Robust MPC.
Robust variants of model predictive control are able to account for set bounded disturbance while still ensuring state constraints are met. Some of the main approaches to robust MPC are given below.
Commercially available MPC software.
Commercial MPC packages are available and typically contain tools for model identification and analysis, controller design and tuning, as well as controller performance evaluation.
A survey of commercially available packages has been provided by S.J. Qin and T.A. Badgwell in "Control Engineering Practice" 11 (2003) 733–764.
MPC vs. LQR.
Model predictive control and linear-quadratic regulators are both expressions of optimal control, with different schemes of setting up optimisation costs.
While a model predictive controller often looks at fixed length, often graduatingly weighted sets of error functions, the linear-quadratic regulator looks at all linear system inputs and provides the transfer function that will reduce the total error across the frequency spectrum, trading off state error against input frequency.
Due to these fundamental differences, LQR has better global stability properties, but MPC often has more locally optimal[?] and complex performance.
The main differences between MPC and LQR are that LQR optimizes across the entire time window (horizon) whereas MPC optimizes in a receding time window, and that with MPC a new solution is computed often whereas LQR uses the same single (optimal) solution for the whole time horizon. Therefore, MPC typically solves the optimization problem in a smaller time window than the whole horizon and hence may obtain a suboptimal solution. However, because MPC makes no assumptions about linearity, it can handle hard constraints as well as migration of a nonlinear system away from its linearized operating point, both of which are major drawbacks to LQR.
This means that LQR can become weak when operating away from stable fixed points. MPC can chart a path between these fixed points, but convergence of a solution is not guaranteed, especially if thought as to the convexity and complexity of the problem space has been neglected.


DFM analysis for stereolithography

In design for additive manufacturing (DFAM), there are both broad themes (which apply to many additive manufacturing processes) and optimizations specific to a particular AM process. Described here is DFM analysis for stereolithography, in which design for manufacturability (DFM) considerations are applied in designing a part (or assembly) to be manufactured by the stereolithography (SLA) process. In SLA, parts are built from a photocurable liquid resin that cures when exposed to a laser beam that scans across the surface of the resin (photopolymerization). Resins containing acrylate, epoxy, and urethane are typically used. Complex parts and assemblies can be directly made in one go, to a greater extent than in earlier forms of manufacturing such as casting, forming, metal fabrication, and machining. Realization of such a seamless process requires the designer to take in considerations of manufacturability of the part (or assembly) by the process. In any product design process, DFM considerations are important to reduce iterations, time and material wastage.
Challenges in stereolithography.
Material.
Excessive setup specific material cost and lack of support for 3rd party resins is a major challenge with SLA process:. The choice of material (a design process) is restricted by the supported resin. Hence, the mechanical properties are also fixed. When scaling up dimensions selectively to deal with expected stresses, post curing is done by further treatment with UV light and heat. Although advantageous to mechanical properties, the additional polymerization and cross linkage can result in shrinkage, warping and residual thermal stresses. Hence, the part shall be designed in its 'green' stage i.e. pre-treatment stage.
Setup and process.
SLA process is an additive manufacturing process. Hence, design considerations such as orientation, process latitude, support structures etc. have to be considered.
Orientation affects the support structures, manufacturing time, part quality and part cost. Complex structures may fail to manufacture properly due to orientation which is not feasible resulting in undesirable stresses. This is when the DFM guidelines can be applied. Design feasibility for stereolithography can be validated by analytical as well as on the basis of simulation and/or guidelines
Rule-based DFM considerations.
Rule-based considerations in DFM refer to certain criteria that the part has to meet in order to avoid failures during manufacturing. Given the layer-by-layer manufacturing technique the process follows, there isn't any constraint on the overall complexity that the part may have. But some rules have been developed through experience by the printer developer/academia which must be followed to ensure that the individual features that make up the part are within certain 'limits of feasibility'.
Printer constraints.
Constraints/limitations in SLA manufacturing comes from the printer's accuracy, layer thickness, speed of curing, speed of printing etc. Various printer constraints are to be considered during design such as:
Support structures.
A point needs support if:
While printing, support structures act as a part of design hence, their limitations and advantages are kept in mind while designing. Major considerations include:
Part deposition orientation.
Part orientation is a very crucial decision in DFM analysis for SLA process. The build time, surface quality, volume/number of support structures etc. depend on this. In many cases, it is also possible to address the manufacturability issues just by reorienting the part. For example, an overhanging geometry with shallow angle may be oriented to ensure steep angles. Hence, major considerations include:
Plan-based DFM considerations.
Plan-based considerations in DFM refer to criteria that arise due to process plan. These are to be met in order to avoid failures during manufacturing of a part that may be satisfy the rule-based criteria but may have some manufacturing difficulties due to sequence in which features are produced.
Geometric tailoring.
Geometric Tailoring bridges the mismatch of material properties and process differences described above. Both functionality and manufacturability issues are addressed. Functionality issues are addressed through 'tailoring' of dimensions of the part to compensate the stress and deflection behavior anomalies. Manufacturability issues are tackled through identification of difficult to manufacture geometric attributes (an approach used in most DFM handbooks) or through simulations of manufacturing processes. For RP-produced parts (as in SLA), the problem formulations are called material-process geometric tailoring (MPGT)/RP.
First, the designer specifies information such as: Parametric CAD model of the part; constraints and goals on functional, geometry, cost and time characteristics; analysis models for these constraints and goals; target values of goals; and preferences for the goals.
DFM problem is then formulated as the designer fills in the MPGT template with this information and sends to the manufacturer, who fills in the remaining 'manufacturing relevant' information. With the completed formulation, the manufacturer is now able to solve the DFM problem, performing GT of the part design. Hence, the MPGT serves as the digital interface between the designer and the manufacturer.
Various Process Planning (PP) strategies have been developed for geometric tailoring in SLA process.
DFM frameworks.
The constraints imposed by the manufacturing process are mapped onto the design. This helps in identification of DFM problems while exploring process plans by acting as a retrieval method. Various DFM frameworks are developed in literature. These frameworks help in various decision making steps such as:
External links.
Dfm2U Live


Slippery road training

Slippery road training is the driving on a closed area with a slippery surface as a part of training road users in driving on slippery roads.
It is used in some countries as a mandatory prerequisite for a driving test, or by drivers who wish to practice their maneuvering skills in slippery conditions. Such training can also detect faults in the brakes or steering of a vehicle which can have a major impact on emergency maneuvers.
Track construction.
In order to be able to simulate wet icy conditions all year around, slippery tracks have traditionally been made using iron plates on the ground upon which an oil film is sprayed. On newer courses, epoxy is often used instead, which only needs to be applied with water to achieve the same effect.
Training requirement for driving license.
Norway.
In Norway, slippery road training is a mandatory part of training which must be completed for everyone taking their driving test, and goes under the name "glattkjøring" (or officially: "sikkerhetskurs på bane"). The exam task consists of regaining control of the vehicle after skidding when braking or turning, as well as adapting driving behavior on slippery roads. A standard slippery track therefore has a long straight for braking, and a curve for turning training. Some courses also have a slippery slope. Normally, a slippery road also has markers in cardboard or similar soft material which can be remotely controlled by the driving instructor to simulate obstacles in the road that the driver must avoid (e.g. a running moose or pedestrians). The Norwegian Automobile Federation owns and operates 26 slippery road tracks in Norway.


Sensitivity (control systems)

In control engineering, the sensitivity (or more precisely, the sensitivity function) of a control system measures how variations in the plant parameters affects the closed-loop transfer function. Since the controller parameters are typically matched to the process characteristics and the process may change, it is important that the controller parameters are chosen in such a way that the closed loop system is not sensitive to variations in process dynamics. Moreover, the sensitivity function is also important to analyse how disturbances affects the system.
Sensitivity function.
Let formula_1 and formula_2 denote the plant and controller's transfer function in a basic closed loop control system written in the Laplace domain using unity negative feedback.
Sensitivity function as a measure of robustness to parameter variation.
The closed-loop transfer function is given by
formula_3
Differentiating formula_4 with respect to formula_5 yields
formula_6
where formula_7 is defined as the function
formula_8
and is known as the sensitivity function. Lower values of formula_9 implies that relative errors in the plant parameters has less effects in the relative error of the closed-loop transfer function.
Sensitivity function as a measure of disturbance attenuation.
The sensitivity function also describes the transfer function from external disturbance to process output. In fact, assuming an additive disturbance "n" after the output
of the plant, the transfer functions of the closed loop system are given by
formula_10
Hence, lower values of formula_9 suggest further attenuation of the external disturbance. The sensitivity function tells us how the disturbances are influenced by feedback. Disturbances with frequencies such that formula_12 is less than one are reduced by an amount equal to the distance to the critical point formula_13 and disturbances with frequencies such that formula_12 is larger than one are amplified by the feedback.
Sensitivity peak and sensitivity circle.
Sensitivity peak.
It is important that the largest value of the sensitivity function be limited for a control system. The nominal sensitivity peak formula_15 is defined as
formula_16
and it is common to require that the maximum value of the sensitivity function, formula_15, be in a range of 1.3 to 2.
Sensitivity circle.
The quantity formula_15 is the inverse of the shortest distance from the Nyquist curve of the loop transfer function to the critical point formula_13. A sensitivity formula_15 guarantees that the distance from the critical point to the Nyquist curve is always greater than formula_21 and the Nyquist curve of the loop transfer function is always outside a circle around the critical point formula_22 with the radius formula_21, known as the sensitivity circle. formula_15 defines the maximum value of the sensitivity function and the inverse of formula_15 gives you the shortest distance from the open-loop transfer function formula_26 to the critical point formula_22.


Symbol level

In knowledge-based systems, agents choose actions based on the principle of rationality to move closer to a desired goal. The agent is able to make decisions based on knowledge it has about the world (see knowledge level). But for the agent to actually change its state, it must use whatever means it has available. This level of description for the agent's behavior is the symbol level. The term was coined by Allen Newell in 1982.
For example, in a computer program, the knowledge level consists of the information contained in its data structures that it uses to perform certain actions. The symbol level consists of the program's algorithms, the data structures themselves, and so on.