Category: Control theory

Full state feedback
Full state feedback (FSF), or pole placement, is a method employed in feedback control system theory to place the closed-loop poles of a plant in pre-determined locations in the s-plane. Placing poles
Consensus dynamics
Consensus dynamics or agreement dynamics is an area of research lying at the intersection of systems theory and graph theory. A major topic of investigation is the agreement or consensus problem in mu
Anticausal system
In systems theory, an anticausal system is a hypothetical system with outputs and internal states that depend solely on future input values. Some textbooks and published research literature might defi
Weighting pattern
A weighting pattern for a linear dynamical system describes the relationship between an input and output . Given the time-variant system described by , then the output can be written as , where is the
Return ratio
The return ratio of a dependent source in a linear electrical circuit is the negative of the ratio of the current (voltage) returned to the site of the dependent source to the current (voltage) of a r
Delay differential equation
In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the functio
Motion control
Motion control is a sub-field of automation, encompassing the systems or sub-systems involved in moving parts of machines in a controlled manner. Motion control systems are extensively used in a varie
Supervisory control theory
The supervisory control theory (SCT), also known as the Ramadge–Wonham framework (RW framework), is a method for automatically synthesizing supervisors that restrict the behavior of a plant such that
Hankel singular value
In control theory, Hankel singular values, named after Hermann Hankel, provide a measure of energy for each state in a system. They are the basis for , in which high energy states are retained while l
Distributed parameter system
In control theory, a distributed-parameter system (as opposed to a lumped-parameter system) is a system whose state space is infinite-dimensional. Such systems are therefore also known as infinite-dim
Bicycle and motorcycle dynamics
Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles and their components, due to the forces acting on them. Dynamics falls under a branch of physics known as class
Asymptotic gain model
The asymptotic gain model (also known as the Rosenstark method) is a representation of the gain of negative feedback amplifiers given by the asymptotic gain relation: where is the return ratio with th
Artstein's theorem
Artstein's theorem states that a nonlinear dynamical system in the control-affine form has a differentiable control-Lyapunov function if and only if it admits a regular stabilizing feedback u(x), that
Compensator (control theory)
A compensator is a component in the control system and it is used to regulate another system. In most of the time, it is done by conditioning the input or the output to that system. There are three ty
Robust control
In control theory, robust control is an approach to controller design that explicitly deals with uncertainty. Robust control methods are designed to function properly provided that uncertain parameter
Lyapunov equation
In control theory, the discrete Lyapunov equation is of the form where is a Hermitian matrix and is the conjugate transpose of . The continuous Lyapunov equation is of the form . The Lyapunov equation
Double integrator
In systems and control theory, the double integrator is a canonical example of a second-order control system. It models the dynamics of a simple mass in one-dimensional space under the effect of a tim
Separation principle in stochastic control
The separation principle is one of the fundamental principles of stochastic control theory, which states that the problems of optimal control and state estimation can be decoupled under certain condit
Class kappa function
In control theory, it is often required to check if a is stable or not. To cope with this it is necessary to use some special comparison functions. Class functions belong to this family: Definition: a
Process control
An industrial process control in continuous production processes is a discipline that uses industrial control systems to achieve a production level of consistency, economy and safety which could not b
Magnitude condition
Within engineering control theory, the magnitude condition is a constraint that is satisfied by the locus of points in the s-plane on which closed-loop poles of a system reside. In combination with th
Real-time Control System
Real-time Control System (RCS) is a reference model architecture, suitable for many software-intensive, real-time computing control problem domains. It defines the types of functions needed in a real-
PLL multibit
A PLL multibit or multibit PLL is a phase-locked loop (PLL) which achieves improved performance compared to a unibit PLL by using more bits. Unibit PLLs use only the most significant bit (MSB) of each
Fractional-order control
Fractional-order control (FOC) is a field of control theory that uses the fractional-order integrator as part of the control system design toolkit. The use of fractional calculus (FC) can improve and
Rise time
In electronics, when describing a voltage or current step function, rise time is the time taken by a signal to change from a specified low value to a specified high value. These values may be expresse
Sensitivity (control systems)
The controller parameters are typically matched to the process characteristics and since the process may change, it is important that the controller parameters are chosen in such a way that the closed
Decision theory
Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilitie
Internal model (motor control)
In the subject area of control theory, an internal model is a process that simulates the response of the system in order to estimate the outcome of a system disturbance. The internal model principle w
Joint spectral radius
In mathematics, the joint spectral radius is a generalization of the classical notion of spectral radius of a matrix, to sets of matrices. In recent years this notion has found applications in a large
State-transition equation
The state-transition equation is defined as the solution of the linear homogeneous state equation. The linear time-invariant state equation given by with state vector x, control vector u, vector w of
Impulse vector
An impulse vector is a mathematical tool to graphically design and analyze input shapers that could suppress residual vibration. The impulse vector can be applied for both undamped and underdamped sys
Weighted product model
The weighted product model (WPM) is a popular multi-criteria decision analysis (MCDA) / multi-criteria decision making (MCDM) method. It is similar to the weighted sum model (WSM). The main difference
Control theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the applicati
Self-organized criticality control
In applied physics, the concept of controlling self-organized criticality refers to the control of processes by which a self-organized system dissipates energy. The objective of the control is to redu
Stochastic control
Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the s
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first
Fault detection and isolation
Fault detection, isolation, and recovery (FDIR) is a subfield of control engineering which concerns itself with monitoring a system, identifying when a fault has occurred, and pinpointing the type of
In electronics, a norator is a theoretical linear, time-invariant one-port which can have an arbitrary current and voltage between its terminals. A norator represents a controlled voltage or current s
Time-invariant system
In control theory, a time-invariant (TIV) system has a time-dependent system function that is not a direct function of time. Such systems are regarded as a class of systems in the field of system anal
Angle condition
In mathematics, the angle condition is a constraint that is satisfied by the locus of points in the s-plane on which closed-loop poles of a system reside. In combination with the magnitude condition,
Bilinear transform
The bilinear transform (also known as Tustin's method, after Arnold Tustin) is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to
Learning automaton
A learning automaton is one type of machine learning algorithm studied since 1970s. Learning automata select their current action based on past experiences from the environment. It will fall into the
Linear parameter-varying control
Linear parameter-varying control (LPV control) deals with the control of linear parameter-varying systems, a class of nonlinear systems which can be modelled as parametrized linear systems whose param
Kharitonov's theorem
Kharitonov's theorem is a result used in control theory to assess the stability of a dynamical system when the physical parameters of the system are not known precisely. When the coefficients of the c
Optimal projection equations
In control theory, optimal projection equations constitute necessary and sufficient conditions for a locally optimal reduced-order LQG controller. The linear-quadratic-Gaussian (LQG) control problem i
The S-procedure or S-lemma is a mathematical result that gives conditions under which a particular quadratic inequality is a consequence of another quadratic inequality. The S-procedure was developed
Feed forward (control)
A feed forward (sometimes written feedforward) is an element or pathway within a control system that passes a controlling signal from a source in its external environment to a load elsewhere in its ex
Parallel parking problem
The parallel parking problem is a motion planning problem in control theory and mechanics to determine the path a car must take to parallel park into a parking space. The front wheels of a car are per
Bellman filter
The Bellman filter is an algorithm that estimates the value sequence of hidden states in a state-space model. It is a generalization of the Kalman filter, allowing for nonlinearity in both the state a
Repetitive control
Repetitive Control is a control method developed by a group of Japanese scholars in 1980s. It is based on the Internal Model Principle and used specifically in dealing with periodic signals, for examp
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to feed back into itself. The notion
Control (optimal control theory)
In optimal control theory, a control is a variable chosen by the controller or agent to manipulate state variables, similar to an actual control valve. Unlike the state variable, it does not have a pr
Affect control theory
In control theory, affect control theory proposes that individuals maintain affective meanings through their actions and interpretations of events. The activity of social institutions occurs through m
Proper transfer function
In control theory, a proper transfer function is a transfer function in which the degree of the numerator does not exceed the degree of the denominator. A strictly proper transfer function is a transf
Quantitative feedback theory
In control theory, quantitative feedback theory (QFT), developed by Isaac Horowitz (Horowitz, 1963; Horowitz and Sidi, 1972), is a frequency domain technique utilising the Nichols chart (NC) in order
Machine learning control
Machine learning control (MLC) is a subfield of machine learning, intelligent control and control theorywhich solves optimal control problems with methods of machine learning.Key applications are comp
Legendre pseudospectral method
The Legendre pseudospectral method for optimal control problems is based on Legendre polynomials. It is part of the larger theory of pseudospectral optimal control, a term coined by Ross. A basic vers
Rosenbrock system matrix
In applied mathematics, the Rosenbrock system matrix or Rosenbrock's system matrix of a linear time-invariant system is a useful representation bridging state-space representation and transfer functio
First-order hold
First-order hold (FOH) is a mathematical model of the practical reconstruction of sampled signals that could be done by a conventional digital-to-analog converter (DAC) and an analog circuit called an
Iterative learning control
Iterative Learning Control (ILC) is a method of tracking control for systems that work in a repetitive mode. Examples of systems that operate in a repetitive manner include robot arm manipulators, che
Digital control
Digital control is a branch of control theory that uses digital computers to act as system controllers.Depending on the requirements, a digital control system can take the form of a microcontroller to
Shift-invariant system
A shift invariant system is the discrete equivalent of a time-invariant system, defined such that if is the response of the system to , then is the response of the system to . That is, in a shift-inva
Witsenhausen's counterexample
Witsenhausen's counterexample, shown in the figure below, is a deceptively simple toy problem in decentralized stochastic control. It was formulated by Hans Witsenhausen in 1968. It is a counterexampl
Advanced process control
In control theory, Advanced process control (APC) refers to a broad range of techniques and technologies implemented within industrial process control systems. Advanced process controls are usually de
Masreliez's theorem
Masreliez theorem describes a recursive algorithmwithin the technology of extended Kalman filter, named after the Swedish-American physicist , who is its author. The algorithm estimates the state of a
Cross Gramian
In control theory, the cross Gramian is a Gramian matrix used to determine how controllable and observable a linear system is. For the stable time-invariant linear system the cross Gramian is defined
Positive systems
Positive systems constitute a class of systems that has the important property that its state variables are never negative, given a positive initial state. These systems appear frequently in practical
Frequency response
In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response i
Differential game
In game theory, differential games are a group of problems related to the modeling and analysis of conflict in the context of a dynamical system. More specifically, a state variable or variables evolv
Hierarchical control system
A hierarchical control system (HCS) is a form of control system in which a set of devices and governing software is arranged in a hierarchical tree. When the links in the tree are implemented by a com
Online model
An online model is a mathematical model which tracks and mirrors a plant or process in real-time, and which is implemented with some form of automatic adaptivity to compensate for model degradation ov
Parasitic oscillation
Parasitic oscillation is an undesirable electronic oscillation (cyclic variation in output voltage or current) in an electronic or digital device. It is often caused by feedback in an amplifying devic
4D-RCS Reference Model Architecture
The 4D/RCS Reference Model Architecture is a reference model for military unmanned vehicles on how their software components should be identified and organized. The 4D/RCS has been developed by the In
Active disturbance rejection control
Active disturbance rejection control (or ADRC) inherits from proportional–integral–derivative (PID). It embraces the power of nonlinear feedback and puts it to full use. It is a robust control method
Perceptual control theory
Perceptual control theory (PCT) is a model of behavior based on the properties of negative feedback control loops. A control loop maintains a sensed variable at or near a reference value by means of t
System analysis
System analysis in the field of electrical engineering characterizes electrical systems and their properties. System analysis can be used to represent almost anything from population growth to audio s
Obstacle avoidance
In robotics, obstacle avoidance is the task of satisfying some control objective subject to non-intersection or non-collision position constraints. What is critical about obstacle avoidance concept in
Space vector modulation
Space vector modulation (SVM) is an algorithm for the control of pulse-width modulation (PWM). It is used for the creation of alternating current (AC) waveforms; most commonly to drive 3 phase AC powe
Multiple models
In control theory, multiple models is an approach to improve efficiency of adaptive system or observer system. It uses large number of models, which are distributed in the region of uncertainty, and b
Transfer function matrix
In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) sy
Dynamic simulation
Dynamic simulation (or dynamic system simulation) is the use of a computer program to model the time-varying behavior of a dynamical system. The systems are typically described by ordinary differentia
Inerter (mechanical networks)
In the study of mechanical networks in control theory, an inerter is a two-terminal device in which the forces applied at the terminals are equal, opposite, and proportional to relative acceleration b
Bellman pseudospectral method
The Bellman pseudospectral method is a pseudospectral method for optimal control based on Bellman's principle of optimality. It is part of the larger theory of pseudospectral optimal control, a term c
Sampled data system
In systems science, a sampled-data system is a control system in which a continuous-time plant is controlled with a digital device. Under periodic sampling, the sampled-data system is time-varying but
Ross–Fahroo lemma
Named after I. Michael Ross and F. Fahroo, the Ross–Fahroo lemma is a fundamental result in optimal control theory. It states that dualization and discretization are, in general, non-commutative opera
Energy-shaping control
Energy-shaping control for energy systems considers the plant and its controller as energy-transformation devices. The control strategy is formulated in terms of interconnection (in a power-preserving
Kalman decomposition
In control theory, a Kalman decomposition provides a mathematical means to convert a representation of any linear time-invariant (LTI) control system to a form in which the system can be decomposed in
Servo bandwidth
Servo bandwidth is the maximum trackable sinusoidal frequency of amplitude A, with tracking achieved at or before 10% of A amplitude is reached. The servo bandwidth indicates the capability of the ser
Filtering problem (stochastic processes)
In the theory of stochastic processes, filtering describes the problem of determining the state of a system from an incomplete and potentially noisy set of observations. While originally motivated by
Flat pseudospectral method
The flat pseudospectral method is part of the family of the Ross–Fahroo pseudospectral methods introduced by Ross and Fahroo. The method combines the concept of differential flatness with pseudospectr
Minimal realization
In control theory, given any transfer function, any state-space model that is both controllable and observable and has the same input-output behaviour as the transfer function is said to be a minimal
Sylvester equation
In mathematics, in the field of control theory, a Sylvester equation is a matrix equation of the form: Then given matrices A, B, and C, the problem is to find the possible matrices X that obey this eq
Switching Kalman filter
The switching Kalman filtering (SKF) method is a variant of the Kalman filter. In its generalised form, it is often attributed to Kevin P. Murphy, but related switching state-space models have been in
Dead-beat control
In discrete-time control theory, the dead-beat control problem consists of finding what input signal must be applied to a system in order to bring the output to the steady state in the smallest number
Recursive economics
Recursive economics is a branch of modern economics based on a paradigm of individuals making a series of two-period optimization decisions over time.
Generalized filtering
Generalized filtering is a generic Bayesian filtering scheme for nonlinear state-space models. It is based on a variational principle of least action, formulated in generalized coordinates of motion.
Concurrent estimation
In discrete event simulation concurrent estimation is a technique used to estimate the effect of alternate parameter settings on a discrete event system. For example from observation of a (computer si
A deadband or dead-band (also known as a dead zone or a neutral zone) is a band of input values in the domain of a transfer function in a control system or signal processing system where the output is
Time-variant system
A time-variant system is a system whose output response depends on moment of observation as well as moment of input signal application. In other words, a time delay or time advance of input not only s
Negative feedback
Negative feedback (or balancing feedback) occurs when some function of the output of a system, process, or mechanism is fed back in a manner that tends to reduce the fluctuations in the output, whethe
Reed receiver
A reed receiver or tuned reed receiver (US) was a form of multi-channel signal decoder used for early radio control systems. It uses a simple electromechanical device or 'resonant reed' to demodulate
Minor loop feedback
Minor loop feedback is a classical method used to design stable robust linear feedback control systems using feedback loops around sub-systems within the overall feedback loop. The method is sometimes
Tensor product model transformation
In mathematics, the tensor product (TP) model transformation was proposed by Baranyi and Yam as key concept for higher-order singular value decomposition of functions. It transforms a function (which
Control (management)
Control is a function of management which helps to check errors in order to take corrective actions. This is done to minimize deviation from standards and ensure that the stated goals of the organizat
Youla–Kucera parametrization
In control theory the Youla–Kučera parametrization (also simply known as Youla parametrization) is a formula that describes all possible stabilizing feedback controllers for a given plant P, as functi
In control engineering a servomechanism, usually shortened to servo, is an automatic device that uses error-sensing negative feedback to correct the action of a mechanism. On displacement-controlled a
Iso-damping is a desirable system property referring to a state where the open-loop phase Bode plot is flat—i.e., the phase derivative with respect to the frequency is zero, at a given frequency calle
Falling cat problem
The falling cat problem is a problem that consists of explaining the underlying physics behind the observation of the cat righting reflex. Although amusing and trivial to pose, the solution of the pro
H-infinity methods in control theory
H∞ (i.e. "H-infinity") methods are used in control theory to synthesize controllers to achieve stabilization with guaranteed performance. To use H∞ methods, a control designer expresses the control pr
A microgrid is a local electrical grid with defined electrical boundaries, acting as a single and controllable entity. It is able to operate in grid-connected and in island mode. A 'Stand-alone microg
Controlled invariant subspace
In control theory, a controlled invariant subspace of the state space representation of some system is a subspace such that, if the state of the system is initially in the subspace, it is possible to
In control theory a self-tuning system is capable of optimizing its own internal running parameters in order to maximize or minimize the fulfilment of an objective function; typically the maximization
Flatness (systems theory)
Flatness in systems theory is a system property that extends the notion of controllability from linear systems to nonlinear dynamical systems. A system that has the flatness property is called a flat
Minimum energy control
In control theory, the minimum energy control is the control that will bring a linear time invariant system to a desired state with a minimum expenditure of energy. Let the linear time invariant (LTI)
Bellman equation
A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the "value" of
Minimum phase
In control theory and signal processing, a linear, time-invariant system is said to be minimum-phase if the system and its inverse are causal and stable. The most general causal LTI transfer function
H square
In mathematics and control theory, H2, or H-square is a Hardy space with square norm. It is a subspace of L2 space, and is thus a Hilbert space. In particular, it is a reproducing kernel Hilbert space
Intelligent control
Intelligent control is a class of control techniques that use various artificial intelligence computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, reinforcem
Ross–Fahroo pseudospectral method
Introduced by I. Michael Ross and F. Fahroo, the Ross–Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control. Examples of the Ross–Fahroo pseudospectral met
American Automatic Control Council
The American Automatic Control Council (AACC) is an organization founded in 1957 for research in control theory. AACC is a member of the International Federation of Automatic Control (IFAC) and is an
Halanay inequality
Halanay inequality is a comparison theorem for differential equations with delay. This inequality and its generalizations have been applied to analyze the stability of delayed differential equations,
Covariance intersection
Covariance intersection is an algorithm for combining two or more estimates of state variables in a Kalman filter when the correlation between them is unknown.
Underactuation is a technical term used in robotics and control theory to describe mechanical systems that cannot be commanded to follow arbitrary trajectories in configuration space. This condition c
H-infinity loop-shaping
H-infinity loop-shaping is a design methodology in modern control theory. It combines the traditional intuition of classical control methods, such as Bode's sensitivity integral, with H-infinity optim
In electronics, a nullator is a theoretical linear, time-invariant one-port defined as having zero current and voltage across its terminals. Nullators are strange in the sense that they simultaneously
Data-driven control system
Data-driven control systems are a broad family of control systems, in which the identification of the process model and/or the design of the controller are based entirely on experimental data collecte
Subspace identification method
In mathematics, specifically in control theory, subspace identification (SID) aims at identifying linear time invariant (LTI) state space models from input-output data. SID does not require that the u
Control reconfiguration
Control reconfiguration is an active approach in control theory to achieve for dynamic systems. It is used when severe faults, such as actuator or sensor outages, cause a break-up of the control loop,
Pfaffian constraint
In dynamics, a Pfaffian constraint is a way to describe a dynamical system in the form: where is the number of equations in a system of constraints. Holonomic systems can always be written in Pfaffian
Coherent control
Coherent control is a quantum mechanics-based method for controlling dynamic processes by light. The basic principle is to control quantum interference phenomena, typically by shaping the phase of las
Zero-order hold
The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC). That is, it describes the effect of converting a disc
Observability Gramian
In control theory, we may need to find out whether or not a system such as is observable, where , , and are, respectively, , , and matrices. One of the many ways one can achieve such goal is by the us
Optogenetics is a biological technique to control the activity of neurons or other cell types with light. This is achieved by expression of light-sensitive ion channels, pumps or enzymes specifically
Input shaping
In control theory, input shaping is an open-loop control technique for reducing vibrations in computer-controlled machines. The method works by creating a command signal that cancels its own vibration
Unscented transform
The unscented transform (UT) is a mathematical function used to estimate the result of applying a given nonlinear transformation to a probability distribution that is characterized only in terms of a
Chain-linked model
The chain-linked model or Kline model of innovation was introduced by mechanical engineer Stephen J. Kline in 1985, and further described by Kline and economist Nathan Rosenberg in 1986. The chain-lin
Networked control system
A networked control system (NCS) is a control system wherein the control loops are closed through a communication network. The defining feature of an NCS is that control and feedback signals are excha
Transient response
In electrical engineering and mechanical engineering, a transient response is the response of a system to a change from an equilibrium or a steady state. The transient response is not necessarily tied
Scenario optimization
The scenario approach or scenario optimization approach is a technique for obtaining solutions to robust optimization and problems based on a sample of the constraints. It also relates to inductive re
Separation principle
In control theory, a separation principle, more formally known as a principle of separation of estimation and control, states that under some assumptions the problem of designing an optimal feedback c
Kalman filter
For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise
Viscous damping
In continuum mechanics, viscous damping is a formulation of the damping phenomena, in which the source of damping force is modeled as a function of the volume, shape, and velocity of an object travers
Terminal sliding mode
In the early 1990s, a new type of sliding mode control, named terminal sliding modes (TSM) was invented at the Jet Propulsion Laboratory (JPL) by Venkataraman and Gulati. TSM is robust non-linear cont
Vector measure
In mathematics, a vector measure is a function defined on a family of sets and taking vector values satisfying certain properties. It is a generalization of the concept of finite measure, which takes
Derivation of the Routh array
The Routh array is a tabular method permitting one to establish the stability of a system using only the coefficients of the characteristic polynomial. Central to the field of control systems design,
Noncommutative signal-flow graph
In automata theory and control theory, branches of mathematics, theoretical computer science and systems engineering, a noncommutative signal-flow graph is a tool for modeling interconnected systems a
Linear–quadratic–Gaussian control
In control theory, the linear–quadratic–Gaussian (LQG) control problem is one of the most fundamental optimal control problems, and it can also be operated repeatedly for model predictive control. It
Hautus lemma
In control theory and in particular when studying the properties of a linear time-invariant system in state space form, the Hautus lemma (after Malo L. J. Hautus), also commonly known as the Popov-Bel
Steady state
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous tim
Glycolytic oscillation
In biochemistry, a glycolytic oscillation is the repetitive fluctuation of in the concentrations of metabolites, classically observed experimentally in yeast and muscle. The first observations of osci
Bartels–Stewart algorithm
In numerical linear algebra, the Bartels–Stewart algorithm is used to numerically solve the Sylvester matrix equation . Developed by R.H. Bartels and G.W. Stewart in 1971, it was the first numerically
Pseudospectral knotting method
In applied mathematics, the pseudospectral knotting method is a generalization and enhancement of a standard pseudospectral method for optimal control. The concept was introduced by I. Michael Ross an
Matched Z-transform method
The matched Z-transform method, also called the pole–zero mapping or pole–zero matching method, and abbreviated MPZ or MZT, is a technique for converting a continuous-time filter design to a discrete-
Hall circles
Hall circles (also known as M-circles and N-circles) are a graphical tool in control theory used to obtain values of a closed-loop transfer function from the Nyquist plot (or the Nichols plot) of the
Ross' π lemma
Ross' π lemma, named after I. Michael Ross, is a result in computational optimal control. Based on generating Carathéodory-π solutions for feedback control, Ross' π-lemma states that there is fundamen
Control system
A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controllin
Process variable
In control theory, a process variable (PV; also process value or process parameter) is the current measured value of a particular part of a process which is being monitored or controlled. An example o
Bode's sensitivity integral
Bode's sensitivity integral, discovered by Hendrik Wade Bode, is a formula that quantifies some of the limitations in feedback control of linear parameter invariant systems. Let L be the loop transfer
Internal environment
The internal environment (or milieu intérieur in French) was a concept developed by Claude Bernard, a French physiologist in the 19th century, to describe the interstitial fluid and its physiological
Moving horizon estimation
Moving horizon estimation (MHE) is an optimization approach that uses a series of measurements observed over time, containing noise (random variations) and other inaccuracies, and produces estimates o
Orbit (control theory)
The notion of orbit of a control system used in mathematical control theory is a particular case of the notion of orbit in group theory.
Servo (radio control)
Servos (also RC servos) are small, cheap, mass-produced servomotors or other actuators used for radio control and small-scale robotics. Most servos are rotary actuators although other types are availa
Supervisory control
Supervisory control is a general term for control of many individual controllers or control loops, such as within a distributed control system. It refers to a high level of overall monitoring of indiv
Singular control
In optimal control, problems of singular control are problems that are difficult to solve because a straightforward application of Pontryagin's minimum principle fails to yield a complete solution. On
Hybrid system
A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior – a system that can both flow (described by a differential equation) and jump (described by a state ma
Integral sliding mode
In 1996, V. Utkin and J. Shi proposed an improved sliding control method named integral sliding mode control (ISMC). In contrast with conventional sliding mode control, the system motion under integra
Head-related transfer function
A head-related transfer function (HRTF), also known as anatomical transfer function (ATF), is a response that characterizes how an ear receives a sound from a point in space. As sound strikes the list
Discrete event dynamic system
In control engineering, a discrete-event dynamic system (DEDS) is a discrete-state, event-driven system of which the state evolution depends entirely on the occurrence of asynchronous discrete events
Dual control theory
Dual control theory is a branch of control theory that deals with the control of systems whose characteristics are initially unknown. It is called dual because in controlling such a system the control
Pulse-swallowing counter
A pulse-swallowing counter is a component in an all-digital feedback system. The divider produces one output pulse for every N counts (N is usually a power of 2) when not swallowing, and per N+1 pulse
Coefficient diagram method
In control theory, the coefficient diagram method (CDM) is an algebraic approach applied to a polynomial loop in the parameter space, where a special diagram called a "coefficient diagram" is used as
Controllability Gramian
In control theory, we may need to find out whether or not a system such as is controllable, where , , and are, respectively, , , and matrices. One of the many ways one can achieve such goal is by the
Impulse response
In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (δ(t)).
Schmidt–Kalman filter
The Schmidt–Kalman Filter is a modification of the Kalman filter for reducing the dimensionality of the state estimate, while still considering the effects of the additional state in the calculation o
Sense and respond
Sense and respond has been used in control theory for several decades, primarily in closed systems such as refineries where comparisons are made between measurements and desired values, and system set
Epistemic feedback
The term "epistemic feedback" is a form of feedback which refers to an interplay between what is being observed (or measured) and the result of the observation.The concept can apply to a process to ob
Adaptive control
Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain. For example, as an aircraft flies, its mass
Loop performance
Loop performance in control engineering indicates the performance of control loops, such as a regulatory PID loop. Performance refers to the accuracy of a control system's ability to track (output) th
Class kappa-ell function
In control theory, it is often required to check if a is stable or not. To cope with this it is necessary to use some special comparison functions. Class functions belong to this family: Definition: A
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 chemica
Particle filter
Particle filters, or sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to solve filtering problems arising in signal processing and Bayesian statistical inference. The filtering
TP model transformation in control theory
Baranyi and Yam proposed the TP model transformation as a new concept in quasi-LPV (qLPV) based control, which plays a central role in the highly desirable bridging between identification and polytopi
Transient state
A system is said to be transient or in a transient state when a process variable or variables have been changed and the system has not yet reached a steady state. The time taken for the circuit to cha
Chebyshev pseudospectral method
The Chebyshev pseudospectral method for optimal control problems is based on Chebyshev polynomials of the first kind. It is part of the larger theory of pseudospectral optimal control, a term coined b
Mason's gain formula
Mason's gain formula (MGF) is a method for finding the transfer function of a linear signal-flow graph (SFG). The formula was derived by Samuel Jefferson Mason, whom it is also named after. MGF is an
Weighted sum model
In decision theory, the weighted sum model (WSM), also called weighted linear combination (WLC) or simple additive weighting (SAW), is the best known and simplest multi-criteria decision analysis (MCD
A nullor is a theoretical two-port network consisting of a nullator at its input and a norator at its output. Nullors represent an ideal amplifier, having infinite current, voltage, transconductance a
Error signal
No description available.
Virtual fixture
A virtual fixture is an overlay of augmented sensory information upon a user's perception of a real environment in order to improve human performance in both direct and remotely manipulated tasks. Dev
Smith predictor
The Smith predictor (invented by O. J. M. Smith in 1957) is a type of predictive controller designed to control systems with a significant feedback time delay. The idea can be illustrated as follows.
Setpoint (control system)
In cybernetics and control theory, a setpoint (SP; also set point) is the desired or target value for an essential variable, or process value (PV) of a control system. Departure of such a variable fro
Data assimilation
Data assimilation is a mathematical discipline that seeks to optimally combine theory (usually in the form of a numerical model) with observations. There may be a number of different goals sought – fo
Krener's theorem
In mathematics, Krener's theorem is a result attributed to Arthur J. Krener in geometric control theory about the topological properties of of finite-dimensional control systems. It states that any at
Intermittent control
Intermittent control is a feedback control method which not only explains some human control systems but also has applications to control engineering. In the context of control theory, intermittent co
Unicycle cart
The term unicycle is often used in robotics and control theory to mean a generalised cart or car moving in a two-dimensional world; these are also often called "unicycle-like" or "unicycle-type" vehic
Bode's ideal transfer function
No description available.
Higher-order sinusoidal input describing function
The higher-order sinusoidal input describing functions (HOSIDF) were first introduced by dr. ir. P.W.J.M. Nuij. The HOSIDFs are an extension of the sinusoidal input describing function which describe