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Control theory for nonlinear or time-variant systems
Nonlinear control theory is an area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary
Nonlinear_control
Advanced method of process control
the nonlinearity. The process can be controlled with nonlinear MPC that uses a nonlinear model directly in the control application. The nonlinear model
Model_predictive_control
Branch of engineering and mathematics
real-world systems because all real control systems are nonlinear. These systems are often governed by nonlinear differential equations. The few mathematical
Control_theory
Mathematical way of attaining a desired output from a dynamic system
t_{f}^{*}]} to the optimal control problem is locally minimizing. A special case of the general nonlinear optimal control problem given in the previous
Optimal_control
Type of control method
control of linear controllers for nonlinear or time-varying processes; Adaptive control or self-tuning control of nonlinear controllers for nonlinear
Adaptive_control
Regulation of nonlinear systems
Linear parameter-varying control (LPV control) deals with the control of linear parameter-varying systems, a class of nonlinear systems which can be modelled
Linear parameter-varying control
Linear_parameter-varying_control
Subfield of machine learning, intelligent control, and control theory
complex nonlinear systems for which linear control theory methods are not applicable. Four types of problems are commonly encountered: Control parameter
Machine_learning_control
Function in control theory
Isidori, A. (1995). Nonlinear Control Systems. Springer. ISBN 978-3-540-19916-8. Freeman, Randy A.; Petar V. Kokotović (2008). "Robust Control Lyapunov Functions"
Control-Lyapunov_function
Engineering discipline that deals with control systems
developments in optimal control in the 1950s and 1960s followed by progress in stochastic, robust, adaptive, nonlinear control methods in the 1970s and
Control_engineering
Approach to control of non-linear systems
In control theory, gain scheduling is an approach to control of nonlinear systems that uses a family of linear controllers, each of which provides satisfactory
Gain_scheduling
Engineering discipline focused on robots
engineers develop adaptive control systems that can modify their behavior in response to changing environments. Nonlinear control techniques are employed
Robotics_engineering
American control theorist
Scopus), with more than 110 papers in each of the two journals. NONLINEAR and ADAPTIVE CONTROL. Krstić’s 1995 book with Kanellakopoulos and Kokotovic, an expanded
Miroslav_Krstić
Method in nonlinear control theory
In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous
Sliding_mode_control
Variable structure control (VSC) is a form of discontinuous nonlinear control. The method alters the dynamics of a nonlinear system by application of
Variable_structure_control
in nonlinear control theory, a non-linear system of the form x ˙ = f ( x , u ) {\displaystyle {\dot {x}}=f(x,u)} is said to satisfy the small control property
Small_control_property
IEEE Control Systems Award. Isidori, A. (1995). Nonlinear Control Systems. Springer. ISBN 978-3-540-19916-8. Isidori, Alberto (1995). Nonlinear Control Systems
Alberto_Isidori
American mathematician and philosopher (1894–1964)
in detail in Nonlinear Problems in Random Theory. Wiener applied Hermite-Laguerre expansion to nonlinear system identification and control. Specifically
Norbert_Wiener
System where changes of output are not proportional to changes of input
a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems
Nonlinear_system
In nonlinear control and stability theory, the circle criterion is a stability criterion for nonlinear time-varying systems. It can be viewed as a generalization
Circle_criterion
Theorem used for studying closed-loop stability
In nonlinear systems, the formalism of input-output stability is an important tool in studying the stability of interconnected systems since the gain
Small-gain_theorem
Property of a dynamical system where solutions near an equilibrium point remain so
typically contain strong nonlinearities not treatable by other methods. A large number of publications appeared then and since in the control and systems literature
Lyapunov_stability
Approach used in controlling nonlinear systems
strategy employed in nonlinear control to control nonlinear systems. Feedback linearization techniques may be applied to nonlinear control systems of the form
Feedback_linearization
In nonlinear control and stability theory, the Popov criterion is a stability criterion discovered by Vasile M. Popov for the absolute stability of a
Popov_criterion
Oscillator that produces a nonsinusoidal repetitive waveform
In electronics, a relaxation oscillator is a nonlinear electronic oscillator circuit that produces a nonsinusoidal repetitive output signal, such as a
Relaxation_oscillator
American electrical engineer, academic and researcher
Learning in Control, Intelligent Control, Nonlinear Control Systems, Robot System Control, Robust and Adaptive Control, Aircraft Control systems, Discrete-Event
Frank_L._Lewis
Robust nonlinear control to achieve exponential stabilization
controllers constitute a class of continuous robust control algorithms developed for nonlinear, control‐affine systems subject to uncertainties and disturbances
RISE_controllers
Disproved conjecture
a disproved conjecture on absolute stability of nonlinear control system with one scalar nonlinearity, which belongs to the sector of linear stability
Kalman's_conjecture
Stability notion for nonlinear control systems with external inputs
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
Input-to-state_stability
Lebanese-Greek-American mathematician
fields of nonlinear stability theory, nonlinear dynamical systems, and nonlinear control and an IEEE Fellow for contributions to robust, nonlinear, and hybrid
Wassim_Michael_Haddad
Rigid pendulum
the smallest perturbation moves the pendulum out of equilibrium. In nonlinear control theory the Kapitza pendulum is used as an example of a parametric
Kapitza's_pendulum
Topics referred to by the same term
Look up nonlinear or nonlinearity in Wiktionary, the free dictionary. Nonlinearity is a property of mathematical functions or data that cannot be graphed
Nonlinearity_(disambiguation)
coupled nonlinear dynamics. The MIT Space Systems Laboratory conducted ground experiments that tested a fully decentralized nonlinear control law, which
Tethered_formation_flying
In nonlinear control, Aizerman's conjecture or Aizerman problem states that a linear system in feedback with a sector nonlinearity would be stable if
Aizerman's_conjecture
Estimation method
mathematical function used to estimate the result of applying a given nonlinear transformation to a probability distribution that is characterized only
Unscented_transform
Professor of engineering at the University of Cambridge and KU Leuven
professor of control engineering in the Control Group at the University of Cambridge and at KU Leuven, with research interests in nonlinear control and neural
Rodolphe_Sepulchre
algorithms optimal control and nonlinear programming." 1977 Walter Murray Wonham "For contributions to multivariable control system theory and design" 1978
List of fellows of IEEE Control Systems Society
List_of_fellows_of_IEEE_Control_Systems_Society
Branch of physics
Nonlinear optics (NLO) is a branch of optics that studies the case when optical properties of matter depend on the intensity of the input light. Nonlinear
Nonlinear_optics
Operator in differential topology
integrability theorem, and is also fundamental in the geometric theory of nonlinear control systems. V. I. Arnold refers to this as the "fisherman derivative"
Lie_bracket_of_vector_fields
Set of philosophical problems
"Zeno hybrid systems" (PDF). International Journal for Robust and Nonlinear Control. 11 (5): 435. doi:10.1002/rnc.592. S2CID 2057416. Archived from the
Zeno's_paradoxes
Use of various control systems for operating equipment
for nonlinear systems (1961), navigation (1960), optimal control and estimation theory (1962), nonlinear control theory (1969), digital control and filtering
Automation
British electronic engineer (1930–2024)
field of control systems engineering. His research interests centred on optimization and optimization-based design, nonlinear control, control of constrained
David_Mayne
Linear optimal control technique
still optimal in a wider class of possibly nonlinear controllers. That is, utilizing a nonlinear control scheme will not improve the expected value of
Linear–quadratic–Gaussian control
Linear–quadratic–Gaussian_control
Egyptian-born American electrical engineer
in nonlinear control and singular perturbation theory, and is widely known for his textbook Nonlinear Systems, which received the 2002 IFAC Control Engineering
Hassan_K._Khalil
professor of systems and control theory at University of Groningen. He is most noted for his contributions to nonlinear control and port-Hamiltonian systems
Arjan_van_der_Schaft
Ralph Kochenburger is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation
Describing_function
Technique for designing controllers
(2013). "On Convergence of the Nonlinear Active Disturbance Rejection Control for MIMO Systems". SIAM Journal on Control and Optimization. 51 (2): 1727–1757
Active disturbance rejection control
Active_disturbance_rejection_control
Technique in nonlinear control theory
and others for designing stabilizing controls for a special class of nonlinear dynamical systems. These systems are built from subsystems that radiate
Backstepping
Control systems and control theory based on negative feedback
system to be controlled. Linear system Linear time-invariant system Nonlinear control "Energy Efficient Design of Auxiliary Systems in Fossil-Fuel Power
Linear_control
Concept in mathematics
these two subsystems independent of each other, thereby simplifying the control problem. Consider a class of system described by the following set of equations:
Singular_perturbation
ISBN 1-85233-378-2. Control theory Manjarekar, N. S.; Banavar, Ravi N. (2012-02-10). Nonlinear Control Synthesis for Electrical Power Systems Using Controllable Series
Energy-shaping_control
Palestinian-Jordanian engineer specialising in non-linear dynamics
as the most influential scholar and scientist in the area of applied nonlinear dynamics in mechanics and engineering. He was the inaugural winner of
Ali_H._Nayfeh
Visual representation used in non-linear control system analysis
In applied mathematics, in particular the context of nonlinear system analysis, a phase plane is a visual display of certain characteristics of certain
Phase_plane
Variable structure control Sliding mode control Hybrid system Nonlinear control Robust control Optimal control H-bridge – A topology that combines four
Variable_structure_system
Discipline that uses industrial control to achieve a production level of consistency
transform Linear parameter-varying control Measurement instruments Model predictive control Negative feedback Nonlinear control Open-loop controller Operational
Industrial_process_control
Filter for nonlinear state estimation
In estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about an estimate of the current
Extended_Kalman_filter
) that is globally asymptotically stable. Nonlinear control Backstepping Khalil, Hassan K. (2002). Nonlinear Systems (3rd ed.). Upper Saddle River, NJ:
Strict-feedback_form
system analysis and control theory. The eminent researchers (born after 1920) include the winners of at least one award of the IEEE Control Systems Award,
List of people in systems and control
List_of_people_in_systems_and_control
In nonlinear control, the technique of Lyapunov redesign refers to the design where a stabilizing state feedback controller can be constructed with knowledge
Lyapunov_redesign
American electrical engineer (1950–2010)
foundational contributions to nonlinear control, output regulation, distributed parameter systems, and geometric methods in control theory. Together with Tryphon
Christopher_I._Byrnes
American control theorist (1938–2023)
outstanding contributions to the theory and practice of linear and nonlinear control systems. Brockett was born on October 22, 1938, in Seville, Ohio,
Roger_W._Brockett
Engineering discipline
electrical engineering). Subfields of control theory include classical control, optimal control, and nonlinear control. Signal processing refers to the generation
Information_engineering
that a nonlinear controller extracts more information from the data than what is possible with a linear control law. Linear-quadratic control problems
Separation principle in stochastic control
Separation_principle_in_stochastic_control
Professor of electrical and computer engineering
Laboratory. His research interests include nonlinear control theory, switched and hybrid dynamical systems, control with limited information, and uncertain
Daniel_Liberzon
In stability theory and nonlinear control, Massera's lemma, named after José Luis Massera, deals with the construction of the Lyapunov function to prove
Massera's_lemma
Topics referred to by the same term
(chemistry) Passivation (spacecraft) Feedback passivation, a concept in nonlinear control This disambiguation page lists articles associated with the title
Passivation
this system, there exist nonlinear control laws that outperform all linear laws. The problem of finding the optimal control law remains unsolved. The
Witsenhausen's_counterexample
dynamic modeling (EDM) is a framework for analysis and prediction of nonlinear dynamical systems. Applications include population dynamics, ecosystem
Empirical_dynamic_modeling
Optimality condition in optimal control theory
(HJB) equation is a nonlinear partial differential equation that provides necessary and sufficient conditions for optimality of a control with respect to
Hamilton–Jacobi–Bellman equation
Hamilton–Jacobi–Bellman_equation
Optimization process
MHE requires an iterative approach that relies on linear programming or nonlinear programming solvers to find a solution. MHE reduces to the Kalman filter
Moving_horizon_estimation
Norwegian professor
(born 28 January 1969) is a Norwegian control systems researcher known for her contributions to nonlinear control and robotics, particularly snake robots
Kristin_Ytterstad_Pettersen
Study of making products from raw materials
submarines. Process control: model predictive control, controllability measures, robust control, nonlinear control, statistical process control, process monitoring
Process_engineering
Technique in mathematical modeling
Framework [1]. Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification
Model_order_reduction
Polish-Canadian scientist and professor (1934 - 1997)
Zames". In B. A. Francis (ed.). Feedback Control, Nonlinear Systems, and Complexity. Lecture Notes in Control and Information Sciences. Vol. 202. Berlin:
George_Zames
Dynamic system property
D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems. Isidori, Alberto (1989). Nonlinear Control Systems, p. 92–3. Springer-Verlag
Controllability
German physicist
is closed-loop flow control for transport systems. Focus is placed on machine learning control and model-based nonlinear control using reduced-order modelling
Bernd_Noack
Serbian control theorist (born 1934)
made contributions in the areas of adaptive control, singular perturbation techniques, and nonlinear control especially the backstepping stabilization method
Petar_V._Kokotovic
D.M.; Zergeroglu, E.; Behal, A. (2001). Nonlinear Control of Wheeled Mobile Robots. Lecture Notes in Control and Information Sciences. Vol. 262. Springer
Warren_E._Dixon
Gameplay involving unordered sequences
A video game with nonlinear gameplay presents players with challenges that can be completed in a number of different sequences. Each may take on (or even
Nonlinear_gameplay
Artificial intelligence control techniques
Neural network control basically involves two steps: System identification Control It has been shown that a feedforward network with nonlinear, continuous
Intelligent_control
Chinese-American control theorist
University, with the dissertation Algebraic Differential Equations and Nonlinear Control Systems supervised by Eduardo D. Sontag. She joined Florida Atlantic
Yuan_Wang_(control_theorist)
Argentine American mathematician
control theory led to the introduction of the concept of input-to-state stability (ISS), a stability theory notion for nonlinear systems, and control-Lyapunov
Eduardo_D._Sontag
American mathematician (born 1942)
Postgraduate School. He has made contributions in the areas of control theory, nonlinear control, and stochastic processes. Krener was born in Brooklyn, New
Arthur_J._Krener
Property of artificial neural networks
Universal approximation power of deep residual neural networks via nonlinear control theory. International Conference on Learning Representations. arXiv:2007
Universal approximation theorem
Universal_approximation_theorem
2019 video game
sectors that can be explored at a nonlinear pace, and players are free to complete side quests and explore hidden areas. Control was completed within three years
Control_(video_game)
Right continuous function with left limits
of a relaxation oscillator". International Journal of Robust and Nonlinear Control. 10 (11–12): 1005–1024. doi:10.1002/1099-1239(200009/10)10:11/12<1005::AID-RNC536>3
Càdlàg
English engineer
(IEEE) in 2015 for contributions to nonlinear control theory. "Congratulations to the 2015 IEEE Fellows". IEEE Control Systems Magazine. 35 (2). IEEE: 23
David_Angeli
Chinese-Canadian mechanical engineer
and Canadian mechanical engineer whose research involves robust and nonlinear control for teleoperation and multi-agent systems. She is a professor of mechanical
Ya-Jun_Pan
nature. Inverted pendulum Robotic unicycle Spinning top Mark W. Spong, Peter Corke, Rogelio Lozano. Nonlinear Control of the Gyroscopic Pendulum. v t e
Inertia_wheel_pendulum
Type of electronic circuit
distorted oscillations of real-world (nonlinear) oscillators are called limit cycles and are studied in nonlinear control theory. In applications where a 'pure'
Electronic_oscillator
Robot control
applied. In this way the complicated nonlinear control problem has been reduced to a relatively simple linear control problem. Lynch, Kevin M.; Park, Frank
Computed_torque_control
Method of quality control
Statistical process control (SPC) or statistical quality control (SQC) is the application of statistical methods to monitor and control the quality of a
Statistical_process_control
Mexican-French control scientist
Mexico, is a Mexican-French control scientist and distinguished professor. He is head of the Adaptive and Nonlinear Control Systems Lab in St. Petersburg
Romeo_Ortega
American control theorist
Kristi A. Morgansen Hill is an American control theorist specializing in nonlinear control and its applications in biologically inspired sensing and motion
Kristi_Morgansen
called a hidden oscillation. In nonlinear control theory, the birth of a hidden oscillation in a time-invariant control system with bounded states means
Hidden_attractor
In control theory, visible state of a system
Eduardo D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems. Lecture notes for Nonlinear Systems Theory by prof. dr. D.Jeltsema
Observability
Concept in theory of differential equations
is a criterion for the asymptotic stability of an autonomous (possibly nonlinear) dynamical system. Suppose a system is represented as x ˙ = f ( x ) {\displaystyle
LaSalle's invariance principle
LaSalle's_invariance_principle
Regression analysis
statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination
Nonlinear_regression
Signal filter whose output is not a linear function of its input
In signal processing, a nonlinear filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals R and
Nonlinear_filter
Modelling language for algebraic equations
nonlinear programming, nonlinear mixed integer programming, dynamic simulation, moving horizon estimation, and nonlinear model predictive control. APMonitor
APMonitor
Type of pendulum
Furuta and his colleagues. It is an example of a complex nonlinear oscillator of interest in control system theory. The pendulum is underactuated and extremely
Furuta_pendulum
NONLINEAR CONTROL
NONLINEAR CONTROL
Girl/Female
Tamil
Self control having complete control on all the senses
Girl/Female
Hindu
Goddess Durga, Self-respecting, Self-controlled, Wise, Sensible
Boy/Male
Tamil
In control of own passions
Girl/Female
Tamil
One who can control senses
Girl/Female
Hindu
Having control upon all abilities
Boy/Male
Hindu
Controller of the senses
Boy/Male
Tamil
Authoritative, Lord, Independent, In control of own passions, Resident of the vindhyas
Boy/Male
Hindu
Victory or ancient philosopher, One who has control over his heart and mind
Boy/Male
Muslim
One who controls her anger
Girl/Female
Indian
One who controls, Suppress
Boy/Male
Hindu
Victory or ancient philosopher, One who has control over his heart and mind
Boy/Male
Tamil
Triyog | தà¯à®°à¯€à®¯à¯‹à®•
Controlling all three dimension
Triyog | தà¯à®°à¯€à®¯à¯‹à®•
Boy/Male
Hindu
One who controls senses
Boy/Male
Hindu
Controller of time
Boy/Male
Hindu
Greek God who controls the winds or west
Boy/Male
Tamil
Desire, Protector, Lord, Another name for Krishna, Controller
Boy/Male
Hindu
Check, Control
Girl/Female
Tamil
Manasvini | மநஸà¯à®µà®¿à®¨à¯€
Goddess Durga, Self-respecting, Self-controlled, Wise, Sensible
Manasvini | மநஸà¯à®µà®¿à®¨à¯€
Girl/Female
Tamil
Indreesha | இநà¯à®¤à¯à®°à®¿à®·à®¾
Having control upon all abilities
Indreesha | இநà¯à®¤à¯à®°à®¿à®·à®¾
Boy/Male
Tamil
Vijitendriya | விஜீதேநà¯à®¤à¯à®°à®¿à®¯Â
Controller of the senses, Lord Hanuman
NONLINEAR CONTROL
NONLINEAR CONTROL
Girl/Female
Arabic, Indian, Muslim, Pashtun, Telugu, Urdu
Angel
Boy/Male
Indian, Punjabi, Sikh
Of Exalted Thoughts and Reflections
Boy/Male
Tamil
Hemaansh = a part of gold
Girl/Female
Tamil
Mist, Fog
Girl/Female
Biblical
Valley of grace.
Male
German
Variant spelling of German Gebhard, GEVEHARD means "gift of strength."
Female
Italian
Feminine form of Italian Saverio, SAVERIA means "a new house."
Girl/Female
Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu
Alert; Sharp Night; Sharp; Moon Light
Boy/Male
Tamil
Name of a sage
Boy/Male
Hindu, Indian, Marathi
Firm; Best of Anything
NONLINEAR CONTROL
NONLINEAR CONTROL
NONLINEAR CONTROL
NONLINEAR CONTROL
NONLINEAR CONTROL
n.
Power or authority to check or restrain; restraining or regulating influence; superintendence; government; as, children should be under parental control.
p. pr. & vb. n.
of Control
n.
Capability of being controlled.
n.
One who, or that which, controls or restraines; one who has power or authority to regulate or control; one who governs.
n.
Specifically, a monarch, or other ruler or master, who uses power to oppress his subjects; a person who exercises unlawful authority, or lawful authority in an unlawful manner; one who by taxation, injustice, or cruel punishment, or the demand of unreasonable services, imposes burdens and hardships on those under his control, which law and humanity do not authorize, or which the purposes of government do not require; a cruel master; an oppressor.
a.
Something that thwarts, crosses, or obstructs; a cross accident; as, he would have succeeded, had it not been for unlucky traverses not under his control.
n.
One whose imagination overpowers his reason and controls his judgment; an unpractical schemer; one who builds castles in the air; a daydreamer.
n.
The power or act of controlling; the state of being restrained; control; restraint; regulation; superintendence.
n.
An iron block, usually bolted to a ship's deck, for controlling the running out of a chain cable. The links of the cable tend to drop into hollows in the block, and thus hold fast until disengaged.
v. t.
To treat as a vassal; to subject to control; to enslave.
n.
Capability of being controlled; controllableness.
a.
Incapable of being controlled; ungovernable; irresistible; as, an uncontrollable temper; uncontrollable events.
a.
Capable of being controlled, checked, or restrained; amenable to command.
a.
Acting contrary to the standard of right; not animated or controlled by justice; false; dishonest; as, an unjust man or judge.
n.
Control of one's self; restraint exercised over one's self; self-command.
n.
The office of a controller.
imp. & p. p.
of Control
adv.
In a lower, subject, or subordinate condition; in subjection; -- used chiefly in a few idiomatic phrases; as, to bring under, to reduce to subjection; to subdue; to keep under, to keep in subjection; to control; to go under, to be unsuccessful; to fail.
a.
Not governed or controlled.
a.
Not accountable or responsible; free from control.