Incremental sheet forming

Incremental sheet forming (or ISF, also known as Single Point Forming) is a sheet metal forming technique where a sheet is formed into the final workpiece by a series of small incremental deformations. However, studies have shown that it can be applied to polymer and composite sheets too. Generally, the sheet is formed by a round tipped tool, typically 5 to 20mm in diameter. The tool, which can be attached to a CNC machine, a robot arm or similar, indents into the sheet by about 1 mm and follows a contour for the desired part. It then indents further and draws the next contour for the part into the sheet and continues to do this until the full part is formed. ISF can be divided into variants depending on the number of contact points between tool, sheet and die (in case there is any). The term Single Point Incremental Forming (SPIF) is used when the opposite side of the sheet is supported by a faceplate and Two Point Incremental Forming (TPIF) when a full or partial die supports the sheet.
Types.
Single-point incremental forming (SPIF) and double-sided incremental forming (DSIF) are the two variants of the IF process. In the DSIF process, two tools are used to form the sheet on either side, while the SPIF process only uses a tool on one side of the sheet. Thus, a component having features on either side of the sheet, e.g., an inverted cone can be effectively formed by the DSIF process.
Advantages over conventional sheet metal forming.
Because the process can be controlled entirely by CNC processes no die is required as is in traditional sheet metal forming. The elimination of the die in the manufacturing process reduces the cost per piece and decreases turnaround time for low production runs because the need to manufacture a die is eliminated. However, for high production runs the time and cost to produce a die is absorbed by the higher per piece speed and lower per piece cost.
Several authors recognize that the formability of metal materials under the localized deformation imposed by incremental forming is better than in conventional deep drawing. In contrast, there is a loss of accuracy with the ISF process.
Implementation.
The ISF process is generally implemented by clamping a sheet in the XY plane, which is free to move along the Z axis. The tool moves in the XY plane and is coordinated with movements in the Z axis to create the desired part. It is often convenient to retrofit a CNC milling machine to accommodate the process. Spherical, flat-bottomed, and parabolic tool profiles can be used to achieve differing surface finishes and forming limits.
The machine employs a combination of stretch forming by drawing the sheet incrementally down over a die, with the CNC tool approach described above. This is said to produce a more even distribution of thickness of the material. The process is well suited to one-off manufacture though difficulties in simulating the process mean that toolpaths are complex and time-consuming to determine.
Ford Motor Company has recently released Ford Freeform Fabrication Technology, a two-point incremental sheet-forming technique being implemented in the rapid prototyping of automotive parts. Complex shapes such as the human face and cranial implants have been manufactured successfully using this manufacturing process. Advances in the technology are expected to increase adoption in the near future by other sheet metal-reliant manufacturers.
Applications.
Incremental forming (IF) is a recent manufacturing process having a wide range of applications in the following areas.
List of process parameters.
The mechanics of the process is influenced by many parameters, including:
Current research.
Research is underway at several universities. The most common implementation is to outfit a traditional milling machine with the spherical tool used in the ISF process. Key research areas include


Hidden Markov random field

In statistics, a hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields have an underlying Markov random field.
Suppose that we observe a random variable formula_1, where formula_2. Hidden Markov random fields assume that the probabilistic nature of formula_1 is determined by the unobservable Markov random field formula_4, formula_2.
That is, given the neighbors formula_6 of formula_7 is independent of all other formula_8 (Markov property).
The main difference with a hidden Markov model is that neighborhood is not defined in 1 dimension but within a network, i.e. formula_4 is allowed to have more than the two neighbors that it would have in a Markov chain. The model is formulated in such a way that given formula_4, formula_1 are independent (conditional independence of the observable variables given the Markov random field).
In the vast majority of the related literature, the number of possible latent states is considered a user-defined constant. However, ideas from nonparametric Bayesian statistics, which allow for data-driven inference of the number of states, have been also recently investigated with success, e.g.


IEC 62264

 IEC 62264 is an international standard for enterprise control system integration. This standard is based upon ANSI/ISA-95.
Current parts of IEC 62264.
IEC 62264 consists of the following parts detailed in separate IEC 62264 standard documents:


October 1865 West Sydney colonial by-election

A by-election was held for the New South Wales Legislative Assembly electorate of West Sydney on 18 October 1865 because of the resignation of John Robertson due to financial difficulties.
Result.

John Robertson resigned due to financial difficulties.


1867 East Sydney colonial by-election

A by-election was held for the New South Wales Legislative Assembly electorate of East Sydney on 20 March 1867 because Charles Cowper resigned due to financial difficulties.
Result.

Charles Cowper resigned due to financial difficulties.


Probe positioning system

A probe positioning system is a tool for the positioning of a (hand-held) measuring device, such as an ultrasound transducer in a fixed, predetermined place to the object, such as a patient. The operation of these systems varies from completely manual, to completely automated.
In (semi-) automated probe positioning systems, a control system corrects for the movement of the object or disturbances in the environment. These systems can use a tilt, pressure or other sensor carried by the probe to collect positional data. The positioner, such as a robotic arm is coupled to the probe. The positioner can provide roll and pitch control as well as translating the probe in lateral and longitudinal directions. A processor receives signals from the sensors corresponding to the actual orientation of the probe and controls the positioner to adjust the orientation of the probe until the desired position is achieved.


The International Federation of Automatic Control (IFAC), founded in September 1957 in France, is a multinational federation of 49 national member organizations (NMO), each one representing the engineering and scientific societies concerned with automatic control in its own country.
The aim of the Federation is to promote the science and technology of control in the broadest sense in all systems, whether, for example, engineering, physical, biological, social or economic, in both theory and application. IFAC is also concerned with the impact of control technology on society.
IFAC pursues its purpose by organizing technical meetings, by publications, and by any other means consistent with its constitution and which will enhance the interchange and circulation of information on automatic control activities.
International World Congresses are held every three years. Between congresses, IFAC sponsors many symposia, conferences and workshops covering particular aspects of automatic control.
The official journals of IFAC are "Automatica", "Control Engineering Practice", "Annual Reviews in Control", "Journal of Process Control", "Engineering Applications of Artificial Intelligence", the "Journal of Mechatronics, Nonlinear Analysis: Hybrid Systems", and the "IFAC Journal of Systems and Control".
Awards.
IFAC Fellows
Major Medals
High Impact Paper Award
Outstanding Service Award


Almen round

An Almen round is a thin round disk used to quantify the intensity of a shot peening process. Developed in 1994 by Rudolf Bosshard in Switzerland, it is a modification of the Almen strip method, which is used worldwide as a surface treatment testing method in the field of shot peening. The basic principle is the same, but due to the simple shape and minimized size, the Almen round is more suitable for automated processing and installation on dummy rigs. Also instead of the Almen block according SAE J442, here a matching device is used and if connected to electronic processing unit, the Almen value according AMS-S-13165 (predecessor MIL-S-13165 Rev.C) can be evaluated in one run.
Test specimen.
The Almen round is a circular cutting from an original Almen strip normally in material SAE 1070. It can be either of a "A", "C" or "N" type offered in various quality grades. The standard strip allows the splitting into four pieces rounds, which have a diameter of 18.7 mm, by either waterjet or laser technique. Therefore, the spaces are maintained in respect of material and thickness. The flatness test to follow is simple and imprecise pieces can be eliminated.
Specimen holder.
In the endeavor to standardize the parameters, the clamping down of the Almen rounds follows a strict geometry. The clamping head fixes the Almen round in correct manner, thus important for all related procedure. When working with the monitoring sensor, the specimen is preloaded to increase overall accuracy.
Measuring technique.
Other than the Almen strip method with the two steps: 1. Processing with holder and 2. Measuring with gage, the Almen round technique combines those activities. The specimen holder is complemented with a measuring system, e.g. a distance sensor system of various kinds to complete the monitoring sensor. While bombarded by shot, the captured Almen round gets bent towards the direction of the attack. The linear transformation gets converted into an electric signal sent to a processing unit. With calibration discs, errors will be minimalized. For the offline measuring of an individual round, the online monitoring sensor or an appropriate device will also be used.
Signal processing.
Thus the equipment is designed for direct exposure to the shot stream, the deformation of the round can be monitored online and directly converted into the Almen standard arc high definition (SAE J443) either in mm or inches. Such a process time will be in the range of less than 5 to 40 seconds. If on screen, the graph shows the basis for the calculation algorithm, also the essential point in mm or inches that is the output information equivalent to the original Almen round definition.
Advanced application.
Many so called "critical parts" require a test run with dummy parts. Therefore the Almen round is captured in a special mount that can be screwed or glued onto the dummy or even on a real part. In such a case an online monitoring is not possible, the specimens must get removed and then measured separately with the monitoring sensor. In this case, only the arc height can be traced. So this application should be in combination with a parallel running online process.
Field of application.
The Almen round can be utilized in aircraft and automotive industry, research and subcontracting peening enterprises.
Application restriction.
As the Almen strip principle has been established in 1942 and international standardization has reached a top-level. The strip work routine is a fixed procedure in practical peening technology. The Almen round principle is more accurate and offers a considerable working time reduction. But as there is no international approved standardization, this technique will be used for special applications only.


Interval predictor model

In regression analysis, an interval predictor model (IPM) is an approach to regression where bounds on the function to be approximated are obtained.
This differs from other techniques in machine learning, where usually one wishes to estimate point values or an entire probability distribution.
Interval Predictor Models are sometimes referred to as a nonparametric regression technique, because a potentially infinite set of functions are contained by the IPM, and no specific distribution is implied for the regressed variables.
Multiple-input multiple-output IPMs for multi-point data commonly used to represent functions have been recently developed. These IPM prescribe the parameters of the model as a path-connected, semi-algebraic set using sliced-normal or sliced-exponential distributions. A key advantage of this approach is its ability to characterize complex parameter dependencies to varying fidelity levels. This practice enables the analyst to adjust the desired level of conservatism in the prediction.
As a consequence of the theory of scenario optimization, in many cases rigorous predictions can be made regarding the performance of the model at test time.
Hence an interval predictor model can be seen as a guaranteed bound on quantile regression.
Interval predictor models can also be seen as a way to prescribe the support of random predictor models, of which a Gaussian process is a specific case
Convex interval predictor models.
Typically the interval predictor model is created by specifying a parametric function, which is usually chosen to be the product of a parameter vector and a basis.
Usually the basis is made up of polynomial features or a radial basis is sometimes used.
Then a convex set is assigned to the parameter vector, and the size of the convex set is minimized such that every possible data point can be predicted by one possible value of the parameters.
Ellipsoidal parameters sets were used by Campi (2009), which yield a convex optimization program to train the IPM.
Crespo (2016) proposed the use of a hyperrectangular parameter set, which results in a convenient, linear form for the bounds of the IPM.
Hence the IPM can be trained with a linear optimization program:
where the training data examples are formula_2 and formula_3, and the Interval Predictor Model bounds formula_4 and formula_5 are parameterised by the parameter vector formula_6.
The reliability of such an IPM is obtained by noting that for a convex IPM the number of support constraints is less than the dimensionality of the trainable parameters, and hence the scenario approach can be applied.
Lacerda (2017) demonstrated that this approach can be extended to situations where the training data is interval valued rather than point valued.
Non-convex interval predictor models.
In Campi (2015) a non-convex theory of scenario optimization was proposed.
This involves measuring the number of support constraints, formula_7, for the Interval Predictor Model after training and hence making predictions about the reliability of the model.
This enables non-convex IPMs to be created, such as a single layer neural network.
Campi (2015) demonstrates that an algorithm where the scenario optimization program is only solved formula_7 times which can determine the reliability of the model at test time without a prior evaluation on a validation set.
This is achieved by solving the optimisation program
where the interval predictor model center line formula_10, and the model width formula_11. This results in an IPM which makes predictions with homoscedastic uncertainty.
Sadeghi (2019) demonstrates that the non-convex scenario approach from Campi (2015) can be extended to train deeper neural networks which predict intervals with hetreoscedastic uncertainty on datasets with imprecision.
This is achieved by proposing generalizations to the max-error loss function given by
which is equivalent to solving the optimisation program proposed by Campi (2015).
Applications.
Initially, scenario optimization was applied to robust control problems.
Crespo (2015) and (2021) applied Interval Predictor Models to the design of space radiation shielding and to system identification.
In Patelli (2017), Faes (2019), and Crespo (2018), Interval Predictor models were applied to the structural reliability analysis problem.
Brandt (2017) applies interval predictor models to fatigue damage estimation of offshore wind turbines jacket substructures.
Garatti (2019) proved that Chebyshev layers (i.e., the minimax layers around functions fitted by linear formula_13-regression) belong to a particular class of Interval Predictor Models, for which the reliability is invariant with respect to the distribution of the data.
Software implementations.
PyIPM provides an open-source Python implementation of the work of Crespo (2015).
OpenCOSSAN provides a Matlab implementation of the work of Crespo (2015).


Sliding mode control

In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces the system to "slide" along a cross-section of the system's normal behavior. The state-feedback control law is not a continuous function of time. Instead, it can switch from one continuous structure to another based on the current position in the state space. Hence, sliding mode control is a variable structure control method. The multiple control structures are designed so that trajectories always move toward an adjacent region with a different control structure, and so the ultimate trajectory will not exist entirely within one control structure. Instead, it will "slide" along the boundaries of the control structures. The motion of the system as it slides along these boundaries is called a "sliding mode" and the geometrical locus consisting of the boundaries is called the "sliding (hyper)surface". In the context of modern control theory, any variable structure system, like a system under SMC, may be viewed as a special case of a hybrid dynamical system as the system both flows through a continuous state space but also moves through different discrete control modes.
Introduction.
Figure 1 shows an example trajectory of a system under sliding mode control. The sliding surface is described by formula_1, and the sliding mode along the surface commences after the finite time when system trajectories have reached the surface. In the theoretical description of sliding modes, the system stays confined to the sliding surface and need only be viewed as sliding along the surface. However, real implementations of sliding mode control approximate this theoretical behavior with a high-frequency and generally non-deterministic switching control signal that causes the system to "chatter" in a tight neighborhood of the sliding surface. Chattering can be reduced through the use of deadbands or boundary layers around the sliding surface, or other compensatory methods. Although the system is nonlinear in general, the idealized (i.e., non-chattering) behavior of the system in Figure 1 when confined to the formula_1 surface is an LTI system with an exponentially stable origin.
One of the compensatory methods is the adaptive sliding mode control method proposed in
 which uses estimated uncertainty to construct continuous control law. In this method chattering is eliminated while preserving accuracy (for more details see references [2] and [3]). The three distinguished features of the proposed adaptive sliding mode controller are as follows: (i) The structured (or parametric) uncertainties and unstructured uncertainties (un-modeled dynamics, unknown external disturbances) are synthesized into a single type uncertainty term called lumped uncertainty. Therefore, a linearly parameterized dynamic model of the system is not required, and the simple structure and computationally efficient properties of this approach make it suitable for the real-time control applications. (ii) The adaptive sliding mode control scheme design relies on the online estimated uncertainty vector rather than relying on the worst-case scenario (i.e., bounds of uncertainties). Therefore, a-priory knowledge of the bounds of uncertainties is not required, and at each time instant, the control input compensates for the uncertainty that exists. (iii) The developed continuous control law using fundamentals of the sliding mode control theory eliminates the chattering phenomena without trade-off between performance and robustness, which is prevalent in boundary-layer approach.
Intuitively, sliding mode control uses practically infinite gain to force the trajectories of a dynamic system to slide along the restricted sliding mode subspace. Trajectories from this reduced-order sliding mode have desirable properties (e.g., the system naturally slides along it until it comes to rest at a desired equilibrium). The main strength of sliding mode control is its robustness. Because the control can be as simple as a switching between two states (e.g., "on"/"off" or "forward"/"reverse"), it need not be precise and will not be sensitive to parameter variations that enter into the control channel. Additionally, because the control law is not a continuous function, the sliding mode can be reached in "finite" time (i.e., better than asymptotic behavior). Under certain common conditions, optimality requires the use of bang–bang control; hence, sliding mode control describes the optimal controller for a broad set of dynamic systems.
One application of sliding mode controller is the control of electric drives operated by switching power converters. Because of the discontinuous operating mode of those converters, a discontinuous sliding mode controller is a natural implementation choice over continuous controllers that may need to be applied by means of pulse-width modulation or a similar technique of applying a continuous signal to an output that can only take discrete states. Sliding mode control has many applications in robotics. In particular, this control algorithm has been used for tracking control of unmanned surface vessels in simulated rough seas with high degree of success.
Sliding mode control must be applied with more care than other forms of nonlinear control that have more moderate control action. In particular, because actuators have delays and other imperfections, the hard sliding-mode-control action can lead to chatter, energy loss, plant damage, and excitation of unmodeled dynamics. Continuous control design methods are not as susceptible to these problems and can be made to mimic sliding-mode controllers.
Control scheme.
Consider a nonlinear dynamical system described by
where
is an -dimensional state vector and
is an -dimensional input vector that will be used for state feedback. The functions formula_5 and formula_6 are assumed to be continuous and sufficiently smooth so that the Picard–Lindelöf theorem can be used to guarantee that solution formula_7 to Equation  exists and is unique.
A common task is to design a state-feedback control law formula_8 (i.e., a mapping from current state formula_7 at time to the input formula_10) to stabilize the dynamical system in Equation  around the origin formula_11. That is, under the control law, whenever the system is started away from the origin, it will return to it. For example, the component formula_12 of the state vector formula_13 may represent the difference some output is away from a known signal (e.g., a desirable sinusoidal signal); if the control formula_10 can ensure that formula_12 quickly returns to formula_16, then the output will track the desired sinusoid. In sliding-mode control, the designer knows that the system behaves desirably (e.g., it has a stable equilibrium) provided that it is constrained to a subspace of its configuration space. Sliding mode control forces the system trajectories into this subspace and then holds them there so that they slide along it. This reduced-order subspace is referred to as a "sliding (hyper)surface", and when closed-loop feedback forces trajectories to slide along it, it is referred to as a "sliding mode" of the closed-loop system. Trajectories along this subspace can be likened to trajectories along eigenvectors (i.e., modes) of LTI systems; however, the sliding mode is enforced by creasing the vector field with high-gain feedback. Like a marble rolling along a crack, trajectories are confined to the sliding mode.
The sliding-mode control scheme involves
Because sliding mode control laws are not continuous, it has the ability to drive trajectories to the sliding mode in finite time (i.e., stability of the sliding surface is better than asymptotic). However, once the trajectories reach the sliding surface, the system takes on the character of the sliding mode (e.g., the origin formula_17 may only have asymptotic stability on this surface).
The sliding-mode designer picks a "switching function" formula_18 that represents a kind of "distance" that the states formula_13 are away from a sliding surface.
The sliding-mode-control law switches from one state to another based on the "sign" of this distance. So the sliding-mode control acts like a stiff pressure always pushing in the direction of the sliding mode where formula_22.
Desirable formula_7 trajectories will approach the sliding surface, and because the control law is not continuous (i.e., it switches from one state to another as trajectories move across this surface), the surface is reached in finite time. Once a trajectory reaches the surface, it will slide along it and may, for example, move toward the formula_25 origin. So the switching function is like a topographic map with a contour of constant height along which trajectories are forced to move.
The sliding (hyper)surface/manifold is typically of dimension formula_26 where is the number of states in formula_13 and is the number of input signals (i.e., control signals) in formula_10. For each control index formula_29, there is an formula_30-dimensional sliding surface given by
The vital part of SMC design is to choose a control law so that the sliding mode (i.e., this surface given by formula_31) exists and is reachable along system trajectories. The principle of sliding mode control is to forcibly constrain the system, by suitable control strategy, to stay on the sliding surface on which the system will exhibit desirable features. When the system is constrained by the sliding control to stay on the sliding surface, the system dynamics are governed by reduced-order system obtained from Equation .
To force the system states formula_13 to satisfy formula_33, one must:
Existence of closed-loop solutions.
Note that because the control law is not continuous, it is certainly not locally Lipschitz continuous, and so existence and uniqueness of solutions to the closed-loop system is "not" guaranteed by the Picard–Lindelöf theorem. Thus the solutions are to be understood in the Filippov sense. Roughly speaking, the resulting closed-loop system moving along formula_33 is approximated by the smooth dynamics formula_38 however, this smooth behavior may not be truly realizable. Similarly, high-speed pulse-width modulation or delta-sigma modulation produces outputs that only assume two states, but the effective output swings through a continuous range of motion. These complications can be avoided by using a different nonlinear control design method that produces a continuous controller. In some cases, sliding-mode control designs can be approximated by other continuous control designs.
Theoretical foundation.
The following theorems form the foundation of variable structure control.
Theorem 1: Existence of sliding mode.
Consider a Lyapunov function candidate
where formula_39 is the Euclidean norm (i.e., formula_40 is the distance away from the sliding manifold where formula_31). For the system given by Equation  and the sliding surface given by Equation , a sufficient condition for the existence of a sliding mode is that
in a neighborhood of the surface given by formula_43.
Roughly speaking (i.e., for the scalar control case when formula_44), to achieve formula_45, the feedback control law formula_46 is picked so that formula_47 and formula_48 have opposite signs. That is,
Note that
and so the feedback control law formula_56 has a direct impact on formula_48.
Reachability: Attaining sliding manifold in finite time.
To ensure that the sliding mode formula_31 is attained in finite time, formula_59 must be more strongly bounded away from zero. That is, if it vanishes too quickly, the attraction to the sliding mode will only be asymptotic. To ensure that the sliding mode is entered in finite time,
where formula_61 and formula_62 are constants.
Explanation by comparison lemma.
This condition ensures that for the neighborhood of the sliding mode formula_63,
So, for formula_65,
which, by the chain rule (i.e., formula_67 with formula_68), means
where formula_70 is the upper right-hand derivative of formula_71 and the symbol formula_72 denotes proportionality. So, by comparison to the curve formula_73 which is represented by differential equation formula_74 with initial condition formula_75, it must be the case that formula_76 for all . Moreover, because formula_77, formula_78 must reach formula_79 in finite time, which means that must reach formula_80 (i.e., the system enters the sliding mode) in finite time. Because formula_78 is proportional to the Euclidean norm formula_82 of the switching function formula_47, this result implies that the rate of approach to the sliding mode must be firmly bounded away from zero.
Consequences for sliding mode control.
In the context of sliding mode control, this condition means that
where formula_39 is the Euclidean norm. For the case when switching function formula_47 is scalar valued, the sufficient condition becomes
Taking formula_88, the scalar sufficient condition becomes
which is equivalent to the condition that
That is, the system should always be moving toward the switching surface formula_91, and its speed formula_92 toward the switching surface should have a non-zero lower bound. So, even though formula_47 may become vanishingly small as formula_13 approaches the formula_31 surface, formula_48 must always be bounded firmly away from zero. To ensure this condition, sliding mode controllers are discontinuous across the formula_91 manifold; they "switch" from one non-zero value to another as trajectories cross the manifold.
Theorem 2: Region of attraction.
For the system given by Equation  and sliding surface given by Equation , the subspace for which the formula_98 surface is reachable is given by
That is, when initial conditions come entirely from this space, the Lyapunov function candidate formula_100 is a Lyapunov function and formula_13 trajectories are sure to move toward the sliding mode surface where formula_102. Moreover, if the reachability conditions from Theorem 1 are satisfied, the sliding mode will enter the region where formula_103 is more strongly bounded away from zero in finite time. Hence, the sliding mode formula_91 will be attained in finite time.
Theorem 3: Sliding motion.
Let
be nonsingular. That is, the system has a kind of controllability that ensures that there is always a control that can move a trajectory to move closer to the sliding mode. Then, once the sliding mode where formula_106 is achieved, the system will stay on that sliding mode. Along sliding mode trajectories, formula_51 is constant, and so sliding mode trajectories are described by the differential equation
If an formula_13-equilibrium is stable with respect to this differential equation, then the system will slide along the sliding mode surface toward the equilibrium.
The "equivalent control law" on the sliding mode can be found by solving
for the equivalent control law formula_56. That is,
and so the equivalent control
That is, even though the actual control formula_10 is not continuous, the rapid switching across the sliding mode where formula_31 forces the system to "act" as if it were driven by this continuous control.
Likewise, the system trajectories on the sliding mode behave as if
The resulting system matches the sliding mode differential equation
, the sliding mode surface formula_31, and the trajectory conditions from the reaching phase now reduce to the above derived simpler condition. Hence, the system can be assumed to follow the simpler formula_119 condition after some initial transient during the period while the system finds the sliding mode. The same motion is approximately maintained when the equality formula_106 only approximately holds.
It follows from these theorems that the sliding motion is invariant (i.e., insensitive) to sufficiently small disturbances entering the system through the control channel. That is, as long as the control is large enough to ensure that formula_45 and formula_48 is uniformly bounded away from zero, the sliding mode will be maintained as if there was no disturbance. The invariance property of sliding mode control to certain disturbances and model uncertainties is its most attractive feature; it is strongly robust.
As discussed in an example below, a sliding mode control law can keep the constraint
in order to asymptotically stabilize any system of the form
when formula_125 has a finite upper bound. In this case, the sliding mode is where
(i.e., where formula_127). That is, when the system is constrained this way, it behaves like a simple stable linear system, and so it has a globally exponentially stable equilibrium at the formula_128 origin.
Control design examples.
Automated design solutions.
Although various theories exist for sliding mode control system design, there is a lack of a highly effective design methodology due to practical difficulties encountered in analytical and numerical methods. A reusable computing paradigm such as a genetic algorithm can, however, be utilized to transform a 'unsolvable problem' of optimal design into a practically solvable 'non-deterministic polynomial problem'. This results in computer-automated designs for sliding model control.
Sliding mode observer.
Sliding mode control can be used in the design of state observers. These non-linear high-gain observers have the ability to bring coordinates of the estimator error dynamics to zero in finite time. Additionally, switched-mode observers have attractive measurement noise resilience that is similar to a Kalman filter. For simplicity, the example here uses a traditional sliding mode modification of a Luenberger observer for an LTI system. In these sliding mode observers, the order of the observer dynamics are reduced by one when the system enters the sliding mode. In this particular example, the estimator error for a single estimated state is brought to zero in finite time, and after that time the other estimator errors decay exponentially to zero. However, as first described by Drakunov, a can be built that brings the estimation error for all estimated states to zero in a finite (and arbitrarily small) time.
Here, consider the LTI system
where state vector formula_180, formula_181 is a vector of inputs, and output is a scalar equal to the first state of the formula_13 state vector. Let
where
The goal is to design a high-gain state observer that estimates the state vector formula_13 using only information from the measurement formula_190. Hence, let the vector formula_191 be the estimates of the states. The observer takes the form
where formula_193 is a nonlinear function of the error between estimated state formula_194 and the output formula_190, and formula_196 is an observer gain vector that serves a similar purpose as in the typical linear Luenberger observer. Likewise, let
where formula_198 is a column vector. Additionally, let formula_199 be the state estimator error. That is, formula_200. The error dynamics are then
where formula_202 is the estimator error for the first state estimate. The nonlinear control law can be designed to enforce the sliding manifold
so that estimate formula_194 tracks the real state formula_12 after some finite time (i.e., formula_206). Hence, the sliding mode control switching function
To attain the sliding manifold, formula_48 and formula_47 must always have opposite signs (i.e., formula_142 for essentially all formula_13). However,
where formula_213 is the collection of the estimator errors for all of the unmeasured states. To ensure that formula_142, let
where
That is, positive constant must be greater than a scaled version of the maximum possible estimator errors for the system (i.e., the initial errors, which are assumed to be bounded so that can be picked large enough; al). If is sufficiently large, it can be assumed that the system achieves formula_217 (i.e., formula_206). Because formula_219 is constant (i.e., 0) along this manifold, formula_220 as well. Hence, the discontinuous control formula_221 may be replaced with the equivalent continuous control formula_222 where
So
This equivalent control formula_222 represents the contribution from the other formula_30 states to the trajectory of the output state formula_12. In particular, the row formula_228 acts like an output vector for the error subsystem
So, to ensure the estimator error formula_230 for the unmeasured states converges to zero, the formula_231 vector formula_232 must be chosen so that the formula_233 matrix formula_234 is Hurwitz (i.e., the real part of each of its eigenvalues must be negative). Hence, provided that it is observable, this formula_230 system can be stabilized in exactly the same way as a typical linear state observer when formula_228 is viewed as the output matrix (i.e., ""). That is, the formula_222 equivalent control provides measurement information about the unmeasured states that can continually move their estimates asymptotically closer to them. Meanwhile, the discontinuous control formula_238 forces the estimate of the measured state to have zero error in finite time. Additionally, white zero-mean symmetric measurement noise (e.g., Gaussian noise) only affects the switching frequency of the control , and hence the noise will have little effect on the equivalent sliding mode control formula_222. Hence, the sliding mode observer has Kalman filter–like features.
The final version of the observer is thus
where
That is, by augmenting the control vector formula_10 with the switching function formula_245, the sliding mode observer can be implemented as an LTI system. That is, the discontinuous signal formula_245 is viewed as a control "input" to the 2-input LTI system.
For simplicity, this example assumes that the sliding mode observer has access to a measurement of a single state (i.e., output formula_190). However, a similar procedure can be used to design a sliding mode observer for a vector of weighted combinations of states (i.e., when output formula_248 uses a generic matrix ). In each case, the sliding mode will be the manifold where the estimated output formula_249 follows the measured output formula_250 with zero error (i.e., the manifold where formula_251).


List of printing protocols

A printing protocol is a protocol for communication between client devices (computers, mobile phones, tablets, etc.) and printers (or print servers). It allows clients to submit one or more print jobs to the printer or print server, and perform tasks such as querying the status of a printer, obtaining the status of print jobs, or cancelling individual print jobs.
Dedicated protocols.
Protocols listed here are specific for printing.
Generic protocols.
These protocols put the printer as similar class to remote disks, scanners and multimedia devices. This is especially true for multi-function printers, that also produce image files (scans and faxes) and send them back through the network.
Wireless protocols.
Wireless protocols is designed for wireless devices. This kind of protocol is based on one kind of printing protocols plus Zero-configuration networking (zeroconf) mechanisms. In this way, printers can be used by wireless devices seamlessly. Note that the printer itself is not necessary to be wireless.
Internet protocols.
The computer and the printer usually should locate in the same local area network (LAN) when using all of the above protocols. Internet printing protocols is designed for Internet printing.
The service ended on December 31, 2020.


Deep reinforcement learning

Deep reinforcement learning (deep RL) is a subfield of machine learning that combines reinforcement learning (RL) and deep learning. RL considers the problem of a computational agent learning to make decisions by trial and error. Deep RL incorporates deep learning into the solution, allowing agents to make decisions from unstructured input data without manual engineering of the state space. Deep RL algorithms are able to take in very large inputs (e.g. every pixel rendered to the screen in a video game) and decide what actions to perform to optimize an objective (e.g. maximizing the game score). Deep reinforcement learning has been used for a diverse set of applications including but not limited to robotics, video games, natural language processing, computer vision, education, transportation, finance and healthcare.
Overview.
Deep learning.
Deep learning is a form of machine learning that utilizes a neural network to transform a set of inputs into a set of outputs via an artificial neural network. Deep learning methods, often using supervised learning with labeled datasets, have been shown to solve tasks that involve handling complex, high-dimensional raw input data such as images, with less manual feature engineering than prior methods, enabling significant progress in several fields including computer vision and natural language processing. In the past decade deep RL has achieved remarkable result on range of problem, from a single and multiplayer games-such as GO, Atari Games, and Dota 2-to robotic
Reinforcement learning.
Reinforcement learning is a process in which an agent learns to make decisions through trial and error. This problem is often modeled mathematically as a Markov decision process (MDP), where an agent at every timestep is in a state formula_1, takes action formula_2, receives a scalar reward and transitions to the next state formula_3 according to environment dynamics formula_4. The agent attempts to learn a policy formula_5, or map from observations to actions, in order to maximize its returns (expected sum of rewards). In reinforcement learning (as opposed to optimal control) the algorithm only has access to the dynamics formula_4 through sampling.
Deep reinforcement learning.
In many practical decision-making problems, the states formula_1 of the MDP are high-dimensional (e.g., images from a camera or the raw sensor stream from a robot) and cannot be solved by traditional RL algorithms. Deep reinforcement learning algorithms incorporate deep learning to solve such MDPs, often representing the policy formula_5 or other learned functions as a neural network and developing specialized algorithms that perform well in this setting.
History.
Along with rising interest in neural networks beginning in the mid 1980s, interest grew in deep reinforcement learning, where a neural network is used in reinforcement learning to represent policies or value functions. Because in such a system, the entire decision making process from sensors to motors in a robot or agent involves a single neural network, it is also sometimes called end-to-end reinforcement learning. One of the first successful applications of reinforcement learning with neural networks was TD-Gammon, a computer program developed in 1992 for playing backgammon. Four inputs were used for the number of pieces of a given color at a given location on the board, totaling 198 input signals. With zero knowledge built in, the network learned to play the game at an intermediate level by self-play and TD(formula_9).
Seminal textbooks by Sutton and Barto on reinforcement learning, Bertsekas and Tsitiklis on neuro-dynamic programming, and others advanced knowledge and interest in the field.
Katsunari Shibata's group showed that various functions emerge in this framework, including image recognition, color constancy, sensor motion (active recognition), hand-eye coordination and hand reaching movement, explanation of brain activities, knowledge transfer, memory, selective attention, prediction, and exploration.
Starting around 2012, the so called Deep learning revolution led to an increased interest in using deep neural networks as function approximators across a variety of domains. This led to a renewed interest in researchers using deep neural networks to learn the policy, value, and/or Q functions present in existing reinforcement learning algorithms.
Beginning around 2013, DeepMind showed impressive learning results using deep RL to play Atari video games. The computer player a neural network trained using a deep RL algorithm, a deep version of Q-learning they termed deep Q-networks (DQN), with the game score as the reward. They used a deep convolutional neural network to process 4 frames RGB pixels (84x84) as inputs. All 49 games were learned using the same network architecture and with minimal prior knowledge, outperforming competing methods on almost all the games and performing at a level comparable or superior to a professional human game tester.
Deep reinforcement learning reached another milestone in 2015 when AlphaGo, a computer program trained with deep RL to play Go, became the first computer Go program to beat a human professional Go player without handicap on a full-sized 19×19 board.
In a subsequent project in 2017, AlphaZero improved performance on Go while also demonstrating they could use the same algorithm to learn to play chess and shogi at a level competitive or superior to existing computer programs for those games, and again improved in 2019 with MuZero. Separately, another milestone was achieved by researchers from Carnegie Mellon University in 2019 developing Pluribus, a computer program to play poker that was the first to beat professionals at multiplayer games of no-limit Texas hold 'em. OpenAI Five, a program for playing five-on-five Dota 2 beat the previous world champions in a demonstration match in 2019.
Deep reinforcement learning has also been applied to many domains beyond games. In robotics, it has been used to let robots perform simple household tasks and solve a Rubik's cube with a robot hand. Deep RL has also found sustainability applications, used to reduce energy consumption at data centers. Deep RL for autonomous driving is an active area of research in academia and industry. Loon explored deep RL for autonomously navigating their high-altitude balloons.
Algorithms.
Various techniques exist to train policies to solve tasks with deep reinforcement learning algorithms, each having their own benefits. At the highest level, there is a distinction between model-based and model-free reinforcement learning, which refers to whether the algorithm attempts to learn a forward model of the environment dynamics.
In model-based deep reinforcement learning algorithms, a forward model of the environment dynamics is estimated, usually by supervised learning using a neural network. Then, actions are obtained by using model predictive control using the learned model. Since the true environment dynamics will usually diverge from the learned dynamics, the agent re-plans often when carrying out actions in the environment. The actions selected may be optimized using Monte Carlo methods such as the cross-entropy method, or a combination of model-learning with model-free methods.
In model-free deep reinforcement learning algorithms, a policy formula_5 is learned without explicitly modeling the forward dynamics. A policy can be optimized to maximize returns by directly estimating the policy gradient but suffers from high variance, making it impractical for use with function approximation in deep RL. Subsequent algorithms have been developed for more stable learning and widely applied. Another class of model-free deep reinforcement learning algorithms rely on dynamic programming, inspired by temporal difference learning and Q-learning. In discrete action spaces, these algorithms usually learn a neural network Q-function formula_11 that estimates the future returns taking action formula_2 from state formula_1. In continuous spaces, these algorithms often learn both a value estimate and a policy.
Research.
Deep reinforcement learning is an active area of research, with several lines of inquiry.
Exploration.
An RL agent must balance the exploration/exploitation tradeoff: the problem of deciding whether to pursue actions that are already known to yield high rewards or explore other actions in order to discover higher rewards. RL agents usually collect data with some type of stochastic policy, such as a Boltzmann distribution in discrete action spaces or a Gaussian distribution in continuous action spaces, inducing basic exploration behavior. The idea behind novelty-based, or curiosity-driven, exploration is giving the agent a motive to explore unknown outcomes in order to find the best solutions. This is done by "modify[ing] the loss function (or even the network architecture) by adding terms to incentivize exploration". An agent may also be aided in exploration by utilizing demonstrations of successful trajectories, or reward-shaping, giving an agent intermediate rewards that are customized to fit the task it is attempting to complete.
Off-policy reinforcement learning.
An important distinction in RL is the difference between on-policy algorithms that require evaluating or improving the policy that collects data, and off-policy algorithms that can learn a policy from data generated by an arbitrary policy. Generally, value-function based methods such as Q-learning are better suited for off-policy learning and have better sample-efficiency - the amount of data required to learn a task is reduced because data is re-used for learning. At the extreme, offline (or "batch") RL considers learning a policy from a fixed dataset without additional interaction with the environment.
Inverse reinforcement learning.
Inverse RL refers to inferring the reward function of an agent given the agent's behavior. Inverse reinforcement learning can be used for learning from demonstrations (or apprenticeship learning) by inferring the demonstrator's reward and then optimizing a policy to maximize returns with RL. Deep learning approaches have been used for various forms of imitation learning and inverse RL.
Goal-conditioned reinforcement learning.
Another active area of research is in learning goal-conditioned policies, also called contextual or universal policies formula_14 that take in an additional goal formula_15 as input to communicate a desired aim to the agent. Hindsight experience replay is a method for goal-conditioned RL that involves storing and learning from previous failed attempts to complete a task. While a failed attempt may not have reached the intended goal, it can serve as a lesson for how achieve the unintended result through hindsight relabeling.
Multi-agent reinforcement learning.
Many applications of reinforcement learning do not involve just a single agent, but rather a collection of agents that learn together and co-adapt. These agents may be competitive, as in many games, or cooperative as in many real-world multi-agent systems. Multi-agent reinforcement learning studies the problems introduced in this setting.
Generalization.
The promise of using deep learning tools in reinforcement learning is generalization: the ability to operate correctly on previously unseen inputs. For instance, neural networks trained for image recognition can recognize that a picture contains a bird even it has never seen that particular image or even that particular bird. Since deep RL allows raw data (e.g. pixels) as input, there is a reduced need to predefine the environment, allowing the model to be generalized to multiple applications. With this layer of abstraction, deep reinforcement learning algorithms can be designed in a way that allows them to be general and the same model can be used for different tasks. One method of increasing the ability of policies trained with deep RL policies to generalize is to incorporate representation learning.


Wireless DNC

Wireless DNC is a form of wireless data transfer, known as Direct Numerical Control, performed between a computer numerical control (CNC) machine and the computer controlling it. These are very widely used in the automobile, engineering, sheet metal and aeronautic industries. These machines are capable of producing different parts. For each type of part, a sequence of instructions is needed. This list of instructions is stored in a computer script, a computer file written in a programming language, such as G-code. This script is commonly referred to as a part program. When a part is to be produced this part program is uploaded to a CNC machine by RS-232 link.
Now this RS-232 link between a PC and CNC machine with software is called a DNC system. In a typical machine shop floor, it is difficult to maintain the data cable. Hence wireless data transfer has come into existence. There are mainly two types of wireless hardware units available in the market. One is using Bluetooth technology, while the other uses Wi-Fi technology.
In case of Bluetooth, generally one pair of Bluetooth devices is used. One gets plugged on a COM port of a PC or Laptop, and the other is connected to an RS-232 port of a CNC machine. The wireless link is established with the required driver software. Once this is established, the user can run their DNC software for data transfer. In most cases, the file is sent from a remote PC to a selected CNC machine.
In Wi-Fi technology, a wireless link is established between a device called wireless access point (generally near the PC) and a device called a wireless node, which is interfaced to the CNC machine. There is one access point and multiple nodes. Each wireless access point and wireless node has one IP address. This IP address must be of the same domain name as the PC. Thus a wireless Ethernet link is created. The wireless node has an RS-232 port, which is connected to an RS-232 port of the CNC machine. Driver software on the PC maps the RS-232 port of the wireless node as a virtual COM port of the PC. Once this is done, the DNC software takes care of the two-way data transfer.


Java Optimized Processor

Java Optimized Processor (JOP)
is a Java processor, an implementation of Java virtual machine (JVM) in hardware.
JOP is free hardware under the GNU General Public License, version 3.
The intention of JOP is to provide a small hardware JVM for embedded real-time systems. The main feature is the predictability of the execution time of Java bytecodes. JOP is implemented over an FPGA.


Signature recognition

Signature recognition is an example of behavioral biometrics that identifies a person based on their handwriting. It can be operated in two different ways:
Static: In this mode, users write their signature on paper, and after the writing is complete, it is digitized through an optical scanner or a camera to turn the signature image into bits. The biometric system then recognizes the signature analyzing its shape. This group is also known as "off-line".
Dynamic: In this mode, users write their signature in a digitizing tablet, which acquires the signature in real time. Another possibility is the acquisition by means of stylus-operated PDAs. Some systems also operate on smart-phones or tablets with a capacitive screen, where users can sign using a finger or an appropriate pen. Dynamic recognition is also known as "on-line". Dynamic information usually consists of the following information:
The state-of-the-art in signature recognition can be found in the last major international competition.
The most popular pattern recognition techniques applied for signature recognition are dynamic time warping, hidden Markov models and vector quantization. Combinations of different techniques also exist.
Related techniques.
Recently, a handwritten biometric approach has also been proposed. In this case, the user is recognized analyzing his handwritten text (see also Handwritten biometric recognition).
Databases.
Several public databases exist, being the most popular ones SVC, and MCYT.


GNU toolchain

The GNU toolchain is a broad collection of programming tools produced by the GNU Project. These tools form a toolchain (a suite of tools used in a serial manner) used for developing software applications and operating systems.
The GNU toolchain plays a vital role in development of Linux, some BSD systems, and software for embedded systems. Parts of the GNU toolchain are also directly used with or ported to other platforms such as Solaris, macOS, Microsoft Windows (via Cygwin and MinGW/MSYS), Sony PlayStation Portable (used by PSP modding scene) and Sony PlayStation 3.
Components.
Projects included in the GNU toolchain are:


LogitBoost

In machine learning and computational learning theory, LogitBoost is a boosting algorithm formulated by Jerome Friedman, Trevor Hastie, and Robert Tibshirani. The original paper casts the AdaBoost algorithm into a statistical framework. Specifically, if one considers AdaBoost as a generalized additive model and then applies the cost function of logistic regression, one can derive the LogitBoost algorithm.
Minimizing the LogitBoost cost function.
LogitBoost can be seen as a convex optimization. Specifically, given that we seek an additive model of the form
the LogitBoost algorithm minimizes the logistic loss:


3D makeR Technologies

3D makeR Technologies (makeR) is a 3D printer manufacturer. The company started out as an open-source printer company. It was founded between Barcelona and Santa Marta by Carlos Camargo, who currently acts as the CEO of the company. Following the traditional RepRap model, the makeR's first products were as do it yourself kits with an alternative version based on open-source FDM 3D printer Prusa i3, called Prusa Tairona. Current makeR 3D printers are designed with a closed frame and selected build sizes.
Products.
Their product line includes the 3D printer series PEGASUS. The makeR 3D printers are compatible with polylactic acid (PLA), acrylonitrile butadiene styrene (ABS), thermoplastic polyurethane (TPU), high-impact polystyrene (HIPS), polyvinyl alcohol (PVA) and some specials materials for industrial needs, such as PLA filament mixed with particles of metals which through sanding 3D printed parts provide appearance similar to metals (steel, copper, and aluminium). Also, makeR printers print with nylon and carbon fiber.


Cast urethanes

Cast Urethanes are similar to injection molding. During the process of injection molding, a hard tool is created. The hard tool, made of an A side and a B side, forms a void within and that void is injected with plastics ranging in material property, durability, and consistency. Plastic cups, dishware, and toys are most commonly made using the process of injection molding because they are common consumer items that need to be produced on a mass scale, and injection molding (once the hard tool has been created) is designed for mass production.
Casting urethanes is similar in that polyurethanes are injected into a tool. But with cast urethanes, the tool is a soft tool, typically made with a type of silicone mold. The mold is created via a master pattern. Master patterns for cast urethanes can be created with CNC machining (which is a common process for injection molding) but cast urethane master patterns are often created with additive manufacturing (or 3D Printing) and the reasons for this vary.
Creating a cast urethane master pattern is different from the steps involved in creating hard tooling for injection molding. Hard tools for injection molding are going to be subjected to a lot of stress and heat during the injection process. They will see runs of thousands of parts per day. The care that goes into a hard tool involves intense machine programming which costs thousands of dollars alone. The price for hard tooling is balanced by the mass production the tooling brings, which is where cast urethanes begin to differ. Cast urethanes are suited for smaller runs of parts and prototyping. Because the cost for soft tooling is lower, down in the hundreds rather than hundreds of thousands, cast urethanes are excellent resources for creators still testing product design, for one-off products, or for testing market and consumer response to a new product.
Master Patterns.
Cast urethane master patterns can be produced using machining, additive manufacturing—even an already existing product. The master pattern is used to create an A side and a B side for a mold. The pattern is used to form a void within a mold. The mold material is one that easily picks up surface detail (such as silicones) because the mold will be responsible for reflecting the surface of the product.
Applications.
There are many types of cast urethane applications including:
Process.
Cast urethane starts as a liquid that can be dispensed into a mold, post cured in ovens and where required, secondary machining operations can be added. Cast thermoset urethanes have better physical properties than most injection or extruded thermoplastics. Dispensing liquid urethane into open molds or compression tools makes it possible to cast just about any configuration from affordable tooling.
Steps include first printing a master pattern for an accurate silicone mold, which is then encased in liquid silicone. After the mold cures, it is cut into distinct sections and the pattern is removed. The cavity formed is used for casting the end product. The cavity or void is filled with a material, which will cure and be removed from the tool.
Industries.
The types of industries that utilize cast urethane include:


Input-to-state stability

Input-to-state stability (ISS) is a stability notion widely used to study stability of nonlinear control systems with external inputs. Roughly speaking, a control system is ISS if it is globally asymptotically stable in the absence of external inputs and if its trajectories are bounded by a function of the size of the input for all sufficiently large times.
The importance of ISS is due to the fact that the concept has bridged the gap between input–output and state-space methods, widely used within the control systems community.
ISS unified the Lyapunov and input-output stability theories and revolutionized our view on stabilization of nonlinear systems, design of robust nonlinear observers, stability of nonlinear interconnected control systems, nonlinear detectability theory, and supervisory adaptive control.
This made ISS the dominating stability paradigm in nonlinear control theory, with such diverse applications as robotics, mechatronics, systems biology, electrical and aerospace engineering, to name a few.
The notion of ISS was introduced for systems described by ordinary differential equations by Eduardo Sontag in 1989.
Since that the concept was successfully used for many other classes of control systems including systems governed by partial differential equations, retarded systems, hybrid systems, etc.
Definition.
Consider a time-invariant system of ordinary differential equations of the form
where formula_1 is a Lebesgue measurable essentially bounded external input and formula_2 is a Lipschitz continuous function w.r.t. the first argument uniformly w.r.t. the second one. This ensures that there exists a unique absolutely continuous solution of the system .
To define ISS and related properties, we exploit the following classes of comparison functions. We denote by formula_3 the set of continuous increasing functions formula_4 with formula_5 and formula_6 the set of continuous strictly decreasing functions formula_4 with formula_8. Then we can denote formula_9 as functions where formula_10 for all formula_11 and formula_12 for all formula_13.
System  is called globally asymptotically stable at zero (0-GAS) if the corresponding system with zero input
is globally asymptotically stable, that is there exist
formula_9 so that for all initial values
formula_15 and all times formula_11 the following estimate is valid for solutions of
System  is called input-to-state stable (ISS) if there exist functions
formula_17 and formula_9 so that for all initial values formula_15, all admissible inputs formula_20 and all times formula_11 the following inequality holds
The function formula_22 in the above inequality is called the gain.
Clearly, an ISS system is 0-GAS as well as BIBO stable (if we put the output equal to the state of the system). The converse implication is in general not true.
It can be also proved that if formula_23, then formula_24.
Characterizations of input-to-state stability property.
For an understanding of ISS its restatements in terms of other stability properties are of great importance.
System  is called globally stable (GS) if there exist
formula_25 such that formula_26, formula_27 and formula_28 it holds that
System  satisfies the asymptotic gain (AG) property if there exists
formula_29: formula_26, formula_27 it holds that
The following statements are equivalent for sufficiently regular right-hand side formula_2
1.  is ISS
2.  is GS and has the AG property
3.  is 0-GAS and has the AG property
The proof of this result as well as many other characterizations of ISS can be found in the papers
 and.
Other characterizations of ISS that are valid under very mild restrictions on the regularity of the rhs formula_2 and are applicable to more general infinite-dimensional systems, have been shown in.
ISS-Lyapunov functions.
An important tool for the verification of ISS are ISS-Lyapunov functions.
A smooth function formula_34 is called an ISS-Lyapunov function for , if formula_35, formula_36 and positive-definite function formula_37, such that:
and
formula_39 it holds:
The function formula_41 is called Lyapunov gain.
If a system  is without inputs (i.e. formula_42), then the last implication reduces to the condition
which tells us that formula_44 is a "classic" Lyapunov function.
An important result due to E. Sontag and Y. Wang is that a system  is ISS if and only if there exists a smooth ISS-Lyapunov function for it.
Examples.
Consider a system
Define a candidate ISS-Lyapunov function formula_46 by
formula_47
formula_48
Choose a Lyapunov gain formula_49 by
Then we obtain that for formula_51 it holds
This shows that formula_44 is an ISS-Lyapunov function for a considered system with the Lyapunov gain formula_49.
Interconnections of ISS systems.
One of the main features of the ISS framework is the possibility to study stability properties of interconnections of input-to-state stable systems.
Consider the system given by
Here formula_55, formula_56 and formula_57 are Lipschitz continuous in formula_58 uniformly with respect to the inputs from the formula_59-th subsystem.
For the formula_59-th subsystem of  the definition of an ISS-Lyapunov function can be written as follows.
A smooth function formula_61 is an ISS-Lyapunov function (ISS-LF)
for the formula_59-th subsystem of , if there exist
functions formula_63, formula_64,
formula_65, formula_66, formula_67 and a positive-definite function formula_68, such that:
and formula_70 it holds
Cascade interconnections.
Cascade interconnections are a special type of interconnection, where the dynamics of the formula_59-th subsystem does not depend on the states of the subsystems formula_73. Formally, the cascade interconnection can be written as
If all subsystems of the above system are ISS, then the whole cascade interconnection is also ISS.
In contrast to cascades of ISS systems, the cascade interconnection of 0-GAS systems is in general not 0-GAS. The following example illustrates this fact. Consider a system given by
Both subsystems of this system are 0-GAS, but for sufficiently large initial states formula_75 and for a certain finite time formula_76 it holds formula_77 for formula_78, i.e. the system  exhibits finite escape time, and thus is not 0-GAS.
Feedback interconnections.
The interconnection structure of subsystems is characterized by the internal Lyapunov gains formula_79. The question, whether the interconnection  is ISS, depends on the properties of the gain operator formula_80 defined by
The following small-gain theorem establishes a sufficient condition for ISS of the interconnection of ISS systems. Let formula_82 be an ISS-Lyapunov function for formula_59-th subsystem of  with corresponding gains formula_79, formula_85. If the nonlinear small-gain condition
holds, then the whole interconnection is ISS.
Small-gain condition  holds iff for each cycle in formula_86 (that is for all formula_87, where formula_88) and for all formula_89 it holds
The small-gain condition in this form is called also cyclic small-gain condition.
Related stability concepts.
Integral ISS (iISS).
System  is called integral input-to-state stable (ISS) if there exist functions formula_91 and formula_9 so that for all initial values formula_15, all admissible inputs formula_20 and all times formula_11 the following inequality holds
In contrast to ISS systems, if a system is integral ISS, its trajectories may be unbounded even for bounded inputs. To see this put formula_96 for all formula_97 and take formula_98. Then the estimate  takes the form
and the right hand side grows to infinity as formula_100.
As in the ISS framework, Lyapunov methods play a central role in iISS theory.
A smooth function formula_34 is called an iISS-Lyapunov function for , if formula_35, formula_36 and positive-definite function formula_37, such that:
and
formula_39 it holds:
An important result due to D. Angeli, E. Sontag and Y. Wang is that system  is integral ISS if and only if there exists an iISS-Lyapunov function for it.
Note that in the formula above formula_37 is assumed to be only positive definite.
It can be easily proved, that if formula_109 is an iISS-Lyapunov function with formula_110, then formula_109 is actually an ISS-Lyapunov function for a system .
This shows in particular, that every ISS system is integral ISS. The converse implication is not true, as the following example shows. Consider the system
This system is not ISS, since for large enough inputs the trajectories are unbounded. However, it is integral ISS with an iISS-Lyapunov function formula_109 defined by
Local ISS (LISS).
An important role are also played by local versions of the ISS property. A system  is called locally ISS (LISS) if there exist a constant formula_115 and functions
formula_17 and formula_9 so that for all formula_118, all admissible inputs formula_119 and all times formula_11 it holds that
An interesting observation is that 0-GAS implies LISS.
Other stability notions.
Many other related to ISS stability notions have been introduced: incremental ISS, input-to-state dynamical stability (ISDS), input-to-state practical stability (ISpS), input-to-output stability (IOS) etc.
ISS of time-delay systems.
Consider the time-invariant time-delay system
Here formula_121 is the state of the system  at time formula_122, formula_123 and formula_124 satisfies certain assumptions to guarantee existence and uniqueness of solutions of the system .
System  is ISS if and only if there exist functions formula_125 and formula_126 such that for every formula_127, every admissible input formula_128 and for all formula_129, it holds that
In the ISS theory for time-delay systems two different Lyapunov-type sufficient conditions have been proposed: via ISS Lyapunov-Razumikhin functions and by ISS Lyapunov-Krasovskii functionals. For converse Lyapunov theorems for time-delay systems see.
ISS of other classes of systems.
Input-to-state stability of the systems based on time-invariant ordinary differential equations is a quite developed theory, see a recent monograph. However, ISS theory of other classes of systems is also being investigated for time-variant ODE systems and hybrid systems. In the last time also certain generalizations of ISS concepts to infinite-dimensional systems have been proposed.
Seminars and online resources on ISS.
1. Online Seminar: Input-to-State Stability and its Applications
2. YouTube Channel on ISS


Prioritised Petri net

A Prioritised Petri net is a structure (PN, Π) where PN is a Petri net and Π is a priority function that maps transitions into non-negative natural numbers representing their priority level
The enabled transitions with a given priority k always fire before any other enabled transition with priority j<k.


Stanford arm

The Stanford arm is an industrial robot with six degrees of freedom, designed at Stanford University by Victor Scheinman in 1969.
The Stanford arm is a serial manipulator whose kinematic chain consists of two revolute joints at the base, a prismatic joint, and a spherical joint. Because it includes several kinematic pairs, it is often used as an educational example in robot kinematics.


Minimum relevant variables in linear system

MINimum Relevant Variables in Linear System (Min-RVLS) is a problem in mathematical optimization. Given a linear program, it is required to find a feasible solution in which the number of non-zero variables is as small as possible.
The problem is known to be NP-hard and even hard to approximate.
Definition.
A Min-RVLS problem is defined by:
The linear system is given by: "A x" "R" "b." It is assumed to be feasible (i.e., satisfied by at least one "x"). Depending on R, there are four different variants of this system: "A x = b, A x ≥ b, A x > b, A x ≠ b".
The goal is to find an "n"-by-1 vector "x" that satisfies the system "A x" "R" "b", and subject to that, contains as few as possible nonzero elements.
Special case.
The problem Min-RVLS[=] was presented by Garey and Johnson, who called it "minimum weight solution to linear equations". They proved it was NP-hard, but did not consider approximations.
Applications.
The Min-RVLS problem is important in machine learning and linear discriminant analysis. Given a set of positive and negative examples, it is required to minimize the number of features that are required to correctly classify them. The problem is known as the minimum feature set problem. An algorithm that approximates Min-RVLS within a factor of formula_1 could substantially reduce the number of training samples required to attain a given accuracy level.
The shortest codeword problem in coding theory is the same problem as Min-RVLS[=] when the coefficients are in GF(2).
Related problems.
In MINimum Unsatisfied Linear Relations (Min-ULR), we are given a binary relation "R" and a linear system "A x" "R" "b", which is now assumed to be "infeasible". The goal is to find a vector "x" that violates as few relations as possible, while satisfying all the others.
Min-ULR[≠] is trivially solvable, since any system with real variables and a finite number of inequality constraints is feasible. As for the other three variants:
In the complementary problem MAXimum Feasible Linear Subsystem (Max-FLS), the goal is to find a maximum subset of the constraints that can be satisfied simultaneously.
Hardness of approximation.
All four variants of Min-RVLS are hard to approximate. In particular all four variants cannot be approximated within a factor of formula_3, for any formula_4, unless NP is contained in DTIME(formula_5). The hardness is proved by reductions:
On the other hand, there is a reduction from Min-RVLS[=] to Min-ULR[=]. It also applies to Min-ULR[≥] and Min-ULR[>], since each equation can be replaced by two complementary inequalities.
Therefore, when R is in {=,>,≥}, Min-ULR and Min-RVLS are equivalent in terms of approximation hardness.


Design for verification

Design for verification (DfV) is a set of engineering guidelines to aid designers in ensuring right first time manufacturing and assembly of large-scale components. The guidelines were developed as a tool to inform and direct designers during early stage design phases to trade off estimated measurement uncertainty against tolerance, cost, assembly, measurability and product requirements.
Background.
Increased competition in the aerospace market has placed additional demands on aerospace manufacturers to reduce costs, increase product flexibility and improve manufacturing efficiency. There is a knowledge gap within the sphere of digital to physical dimensional verification and on how to successfully achieve dimensional specifications within real-world assembly factories that are subject to varying environmental conditions.
The DfV framework is an engineering principle to be used within low rate and high value and complexity manufacturing industries to aid in achieving high productivity in assembly via the effective dimensional verification of large volume structures, during final assembly. The DfV framework has been developed to enable engineers to design and plan the effective dimensional verification of large volume, complex structures in order to reduce failure rates and end-product costs, improve process integrity and efficiency, optimise metrology processes, decrease tooling redundancy and increase product quality and conformance to specification. The theoretical elements of the DfV methods were published in 2016, together with their testing using industrial case studies of representative complexity. The industrial tests published on ScienceDirect proved that by using the new design for verification methods alongside the traditional ‘design for X’ toolbox, the resultant process achieved improved tolerance analysis and synthesis, optimized large volume metrology and assembly processes and more cost-effective tool and jig design.


ZF 5HP transmission

5HP is ZF Friedrichshafen AG's trademark name for its five-speed automatic transmission models (5-speed transmission with Hydraulic converter and Planetary gearsets) for longitudinal engine applications, designed and built by ZF's subsidiary in Saarbrücken.
Specifications.
Final Conventionally Designed Gearbox.
The 5HP is the last transmission family that utilized a conventional design. To meet the requirements for a greater number of gear ratios, the only viable option entailed adding more components. That made these gearboxes bigger, heavier and even more expensive to build. As the presence of up to ten main components (two Ravigneaux gearsets in series, along with brakes and clutches) showed, this marked the end of conventional gearbox design. The successor, the 6HP-family, employed an all-new Lepelletier gear mechanism design, which needed only eight main components in order to achieve six gear ratios. This demonstrated a new paradigm in gearbox design.
Ravigneaux Planetary Gearset Types.
5HP 18.
Applications
5HP 19.
Applications
BMW — longitudinal engine, rear wheel drive
5HP 19FL.
Applications
Volkswagen Group — longitudinal engine transaxle, front-wheel drive
5HP 19FLA.
Applications
Volkswagen Group — longitudinal engine, transaxle permanent four-wheel drive
1999 (DRN/EKX) transmissions used Induction speed sensors and 2000+ (FAS) transmissions used Hall Effect sensors. These transmissions are mechanically the same, but are not interchangeable.
5HP 19HL.
Applications
Porsche — longitudinal engine rear engine transaxle
5HP 19HLA.
Applications
Porsche — longitudinal engine rear engine transaxle
Porsche — mid-engine design flat-six engine, 5-speed tiptronic #1060, rear-wheel drive A87.01-xxx, A87.02-xxx, A87.21-xxx, [5HP19FL Valve Body, Solenoids, and Speed Sensor. Different Wiring Harness.] [Speed Sensor/Pulser part # ZF 0501314432]
Simpson Planetary Gearset Types.
5HP 24.
Applications
5HP 24A.
Applications
5HP 30.
Applications


Instrumentation and control engineering

Instrumentation and control engineering (ICE) is a branch of engineering that studies the measurement and control of process variables, and the design and implementation of systems that incorporate them. Process variables include pressure, temperature, humidity, flow, pH, force and speed.
ICE combines two branches of engineering. Instrumentation engineering is the science of the measurement and control of process variables within a production or manufacturing area. Meanwhile, control engineering, also called control systems engineering, is the engineering discipline that applies control theory to design systems with desired behaviors.
Control engineers are responsible for the research, design, and development of control devices and systems, typically in manufacturing facilities and process plants. Control methods employ sensors to measure the output variable of the device and provide feedback to the controller so that it can make corrections toward desired performance. Automatic control manages a device without the need of human inputs for correction, such as cruise control for regulating a car's speed.
Control systems engineering activities are multi-disciplinary in nature. They focus on the implementation of control systems, mainly derived by mathematical modeling. Because instrumentation and control play a significant role in gathering information from a system and changing its parameters, they are a key part of control loops.
As profession.
High demand for engineering professionals is found in fields associated with process automation. Specializations include industrial instrumentation, system dynamics, process control, and control systems. Additionally, technological knowledge, particularly in computer systems, is essential to the job of an instrumentation and control engineer; important technology-related topics include human–computer interaction, programmable logic controllers, and SCADA. The tasks center around designing, developing, maintaining and managing control systems.
The goals of the work of an instrumentation and control engineer are to maximize:
As academic discipline.
Many universities teach instrumentation and control engineering as an academic courses at the graduate and postgraduate levels. It is possible to approach this field coming from many standard engineering backgrounds, being the most common among them Electrical and Mechanical Engineering, since these branches cover strong foundational subjects in control systems, system dynamics, electro-mechanical machines and devices, as well as electric circuits.


Spillage

In industrial production, spillage is the loss of production output due to production of a series of defective or unacceptable products which must be rejected. Spillage is an often costly event which occurs in manufacturing when a process degradation or failure occurs that is not immediately detected and corrected, and in which defective or reject product therefore continues to be produced for some extended period of time.
Spillage results in costs due to lost production volume, excessive scrap, delayed delivery of product, and wastage of human and capital equipment resources. Minimization of the occurrence and duration of manufacturing spillage requires that closed-loop control and associated process monitoring and metrology functions be integrated into critical steps of the overall manufacturing process. The extent to which process control is complete and metrology is high resolution so as to be comprehensive determines the extent to which spillages will be prevented.


MazaCAM

MazaCAM is a CNC programming system for the Mazak CNC (Numerical control) machine-tools (see Yamazaki Mazak Corporation), sold and supported by SolutionWare Corporation.
MazaCAM differs from most other CNC programming systems in that it can generate CNC programs in both Mazatrol and G-code .
References.
Other Sources of Notability


Set estimation

In statistics, a random vector "x" is classically represented by a probability density function.
In a set-membership approach or set estimation, "x" is represented by a set "X" to which "x" is assumed to belong. This means that the support of the probability distribution function of "x" is included inside "X". On the one hand, representing random vectors by sets makes it possible to provide fewer assumptions on the random variables (such as independence) and dealing with nonlinearities is easier. On the other hand, a probability distribution function provides a more accurate information than a set enclosing its support.
Set-membership estimation.
Set membership estimation (or "set estimation" for short) is an estimation approach which considers that measurements are represented by a set "Y" (most of the time a box of R"m", where "m"
is the number of measurements) of the measurement space. If "p" is the parameter vector and "f" is the model function, then the set of all feasible parameter vectors is
where "P"0 is the prior set for the parameters. Characterizing "P" corresponds to a set-inversion problem.
Resolution.
When "f" is linear the feasible set "P" can be described by linear inequalities and can be approximated using linear programming techniques.
When "f" is nonlinear, the resolution can be performed using interval analysis. The feasible set "P" is then approximated by an inner and an outer subpavings. The main limitation of the method is its exponential complexity with respect to the number of parameters.
Example.
Consider the following model
where "p"1 and "p"2 are the two parameters
to be estimated.
Assume that at times "t"1=−1, "t"2=1, "t"3=2,
the following interval measurements have been collected:
as illustrated by Figure 1. The corresponding measurement set (here a box) is
The model function is defined by
The components of "f" are obtained using the model for each time measurement.
After solving the set inversion problem, we get the approximation depicted on Figure 2.
Red boxes are inside the feasible set "P" and blue boxes are outside "P".
Recursive case.
Set estimation can be used to estimate the state of a system described by state equations using a recursive implementation.
When the system is linear, the corresponding feasible set for the state vector can be described by polytopes or by ellipsoids
When the system is nonlinear, the set can be enclosed by subpavings.
Robust case.
When outliers occur, the set estimation method generally returns an empty set. This is
due to the fact that the intersection between of sets of parameter vectors that are consistent
with the "i"th data bar is empty. To be robust with respect to outliers,
we generally characterize the set of parameter vectors that are consistent with
all data bars except "q" of them. This is possible using the notion of "q"-relaxed intersection.


Machine Sazi Tabriz

Machine Sazi Tabriz Co. (Tabriz Machinery Manufacturing Co.) which is also called by its abbreviation MST, is a Machine tool manufacturing factory in Tabriz, Iran. The major products of the factory are machinery tools such as turning machines, milling machines, drilling machines, grinding machines. A large variety of MST's products are CNC controlled machines. The MST manufacturing complex established on 1969 with technological helps from east European countries. The MST serves as a nationwide base for design and manufacturing of machine tools. MST owns the Machine Sazi football club, since 1969 to now.


Soft sensor

Soft sensor or virtual sensor is a common name for software where several measurements are processed together. Commonly soft sensors are based on control theory and also receive the name of state observer. There may be dozens or even hundreds of measurements. The interaction of the signals can be used for calculating new quantities that need not be measured. Soft sensors are especially useful in data fusion, where measurements of different characteristics and dynamics are combined. It can be used for fault diagnosis as well as control applications.
Well-known software algorithms that can be seen as soft sensors include Kalman filters. More recent implementations of soft sensors use neural networks or fuzzy computing.
Examples of soft sensor applications:


Rapid Heat Cycle Molding

Rapid Heat Cycle Molding (RHCM) is also known as steam injection molding. Dr. Chao-Tsai Huang has written an extensive 68 page paper outlining, among other things, a case study on RHCM. His paper is entitled In-depth Study of RHCM and IHM Technologiesand Industrial Applications.
In general, ABS material is used as the raw material. The primary advantage of steam injection is that it eliminates weld-lines on molded parts. This allows companies to eliminate future processes such as painting. In non-steam molding, water will heat the tool to a constant temperature. Plastic will be injected to the warm tool.
In steam molding, steam is injected at 160 degrees to heat the tool. When the tool reaches a predetermined temperature (about 140 degrees), the plastic is injected. Cold water is immediately added to the process to cool the plastic down to around 40 degrees.
Because the mold is so hot when the plastic is injected, there are no weld lines, and a "perfect" product results. Steam injection molding is now being extensively used to produce the front covers of LCD TVs.


Time metrology

Time metrology or time and frequency metrology is the application of metrology for time keeping, including frequency stability.
Its main tasks are the realization of the second as the SI unit of measurement for time and the establishment of time standards and frequency standards as well as their dissemination.


Castability

Castability is the ease of forming a quality casting. A very castable part design is easily developed, incurs minimal tooling costs, requires minimal energy, and has few rejections. Castability can refer to a part design or a material property.
Part design.
Part design and geometry directly affect the castability, with volume, surface area and the number of features being the most important attributes.
If the design has undercuts or interior cavities it decreases castability due to tooling complexity. Long thin sections in a design are hard to fill. Sudden changes in wall thickness reduce castability because it induces turbulence during filling; fillets should be added to avoid this. Annulars in the path of flow should be avoided because they can cause cold shuts or misruns. A design that causes isolated hot spots decreases castability. An ideal design would have progressive directional solidification from the thinnest section to the thickest.
Location of the mold's parting line also affects castability, because a non-planar parting line also increases tooling complexity.
If a design requires a high degree of accuracy, fine surface finish or defect free surface it reduces the castability of the part. However, the casting process can be very economical for part designs that require intricate contoured surfaces, thickness variations, and internal features.
Quantitative analysis.
The castability of a design can be partially quantitatively determined by the following three equations. Better castability is denoted by a larger number.
Where Vc is the volume of the casting and Vb is the volume of the smallest box that the casting could fit in.
Where Vc is the volume of the casting and Ac is the surface area of the casting
Where nf is the number of features (holes, pockets, slots, bosses, ribs, etc.)
Material properties.
Material properties that influence their castability include their pouring temperature, fluidity, solidification shrinkage, and slag/dross formation tendencies.