Search results for "Linear"

showing 10 items of 7165 documents

Stability analysis and H<inf>∞</inf> controller design of a class of switched discrete-time fuzzy systems

2011

In this paper, the problems of stability analysis and H ∞ controller design of a class of switched nonlinear systems are investigated. In a classical way, the modeling of the systems is approached by switched fuzzy systems, and both fast switching and slow switching are considered there. In particular, for slow switching scheme, a new mode-dependent average dwell time switching is proposed for the underlying switched fuzzy systems. Based on a fuzzy-basis-dependent and mode-dependent Lyapunov function, the H ∞ state-feedback controller is derived. A numerical example is given to show the validity and potential of the theoretical results.

Lyapunov functionNonlinear systemsymbols.namesakeDwell timeDiscrete time and continuous timeControl theoryStability (learning theory)symbolsSymmetric matrixFuzzy control systemMathematicsIEEE Conference on Decision and Control and European Control Conference
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Adaptive Neural Stabilizing Controller for a Class of Mismatched Uncertain Nonlinear Systems by State and Output Feedback

2015

In this paper, first, an adaptive neural network (NN) state-feedback controller for a class of nonlinear systems with mismatched uncertainties is proposed. By using a radial basis function NN (RBFNN), a bound of unknown nonlinear functions is approximated so that no information about the upper bound of mismatched uncertainties is required. Then, an observer-based adaptive controller based on RBFNN is designed to stabilize uncertain nonlinear systems with immeasurable states. The state-feedback and observer-based controllers are based on Lyapunov and strictly positive real-Lyapunov stability theory, respectively, and it is shown that the asymptotic convergence of the closed-loop system to ze…

Lyapunov functionObserver (quantum physics)Computer Simulation; Feedback; Neural Networks (Computer); Nonlinear Dynamics; Control and Systems Engineering; Software; Information Systems; Human-Computer Interaction; Computer Science Applications1707 Computer Vision and Pattern Recognition; Electrical and Electronic EngineeringComputer Science Applications1707 Computer Vision and Pattern RecognitionNeural Networks (Computer)Nonlinear controlUpper and lower boundsFeedbackComputer Science ApplicationsHuman-Computer InteractionNonlinear systemsymbols.namesakeNonlinear DynamicsControl and Systems EngineeringControl theoryAdaptive systemStability theorysymbolsComputer SimulationNeural Networks ComputerElectrical and Electronic EngineeringSoftwareInformation SystemsMathematicsIEEE Transactions on Cybernetics
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Design on fuzzy control for a class of stochastic nonlinear systems

2014

The problem of Hankel-norm output feedback control is solved for a class of T-S fuzzy stochastic systems. The dynamic output feedback controller design technique is proposed by employing fuzzy-basis-dependent Lyapunov function approach and the conversion on the Hankel-norm controller parameters. Sufficient conditions are established to design the controllers such that the resulting closed-loop system is stochastically stable and satisfies a prescribed performance. The desired output feedback controller can be obtained by solving a convex optimization problem, which can be efficiently solved by standard numerical algorithms Refereed/Peer-reviewed

Lyapunov functionOutput feedbackStochastic stabilityClass (computer programming)Mathematical optimizationLMIsStochastic systemsFuzzy control systemFuzzy systemssymbols.namesakeNonlinear systemControl theoryFuzzy systems; LMIs; Stochastic systems; Electrical and Electronic EngineeringConvex optimizationsymbolsElectrical and Electronic EngineeringMathematics
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Analytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu–Morioka System

2015

In applied investigations, the invariance of the Lyapunov dimension under a diffeomorphism is often used. However, in the case of irregular linearization, this fact was not strictly considered in the classical works. In the present work, the invariance of the Lyapunov dimension under diffeomorphism is demonstrated in the general case. This fact is used to obtain the analytic exact upper bound of the Lyapunov dimension of an attractor of the Shimizu–Morioka system. peerReviewed

Lyapunov functionPure mathematicsMathematics::Dynamical SystemsGeneral Physics and Astronomylcsh:AstrophysicsLyapunov exponentUpper and lower boundssymbols.namesakeShimizu-Morioka systemDimension (vector space)Attractorlcsh:QB460-466Lyapunov equationLyapunov redesignlcsh:ScienceMathematicsta111Mathematical analysisShimizu–Morioka systemlcsh:QC1-999Nonlinear Sciences::Chaotic DynamicssymbolsLyapunov dimensionlcsh:QDiffeomorphismLyapunov exponentlcsh:PhysicsEntropy
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Analysis of singular bilinear systems using Walsh functions

1991

The use of Walsh functions to analyse singular bilinear systems is investigated. It is shown that the nonlinear implicit differential system equation may be converted to a set of linear algebraic Lyapunov equations to be solved iteratively for the coefficients of the semistate x(t) in terms of the Walsh basis functions. Solution of the iterative algorithm is uniformly convergent to the exact solution of the algebraic generalised Lyapunov equation of the singular bilinear system. The present method is slightly more complicated than a similar one arising from the analysis of linear singular systems. In fact, it is a hybrid between the analyses of usual linear singular and bilinear regular sys…

Lyapunov functionRegular singular pointMathematical analysisGeneral EngineeringBilinear interpolationBilinear formsymbols.namesakeSingular solutionWalsh functionsymbolsApplied mathematicsLyapunov equationMathematicsSingular point of an algebraic varietyIEE Proceedings D Control Theory and Applications
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Design of unknown inputs proportional integral observers for TS fuzzy models

2014

In this paper the design of unknown inputs proportional integral observers for Takagi-Sugeno (TS) fuzzy models subject to unmeasurable decision variables is proposed. These unknown inputs affect both state and output of the system. The synthesis of these observers is based on two hypotheses that the unknown inputs are under the polynomials form with their kth derivatives zero for the first one and bounded norm for the second one, hence two approaches. The Lyapunov theory and L"2-gain technique are used to develop the stability conditions of such observers in LMIs (linear matrix inequality) formulation. A simulation example is given to validate and compare the proposed design conditions for …

Lyapunov functionUnknown inputs reconstructionCognitive NeuroscienceLinear matrix inequalityComputer Science Applications1707 Computer Vision and Pattern RecognitionFuzzy logicComputer Science ApplicationsStability conditionssymbols.namesakeDecision variablesComputer Science::Systems and ControlArtificial IntelligenceControl theoryBounded functionNorm (mathematics)Unmeasurable decision variablessymbolsTS fuzzy modelsProportional integral observer; TS fuzzy models; Unknown inputs reconstruction; Unmeasurable decision variables; Artificial Intelligence; Computer Science Applications1707 Computer Vision and Pattern Recognition; Cognitive NeuroscienceProportional integral observerMathematicsNeurocomputing
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Input-Output Feedback Linearization Control with On-Line Inductances Estimation of Synchronous Reluctance Motors

2021

This paper proposes an adaptive input-output Feedback Linearization (FL) techniques for Synchronous Reluctance Motor (SynRM) drives, taking into consideration the iron losses. As a main original content, this work proposes a control law based on a new dynamic model of the SynRM including iron losses as well as the on-line estimation of the static inductances. The on-line estimation of the SynRM static inductances permits to inherently take into consideration the magnetic saturation phenomena occuring on both axes. The estimation law is obtained thanks to a Lyapunov-based analysis and thus the stability of the entire control system, including the estimation algorithm, is intrinsically guaran…

Lyapunov functionfeedback linearizationSynchronous reluctance motorMagnetic reluctanceComputer scienceStability (learning theory)Nonlinear systemsymbols.namesakeinductances estimationSettore ING-INF/04 - AutomaticaControl theoryControl systemLine (geometry)symbolsA priori and a posterioriFeedback linearizationAdaptive system
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Adaptive output feedback neural network control of uncertain non-affine systems with unknown control direction

2014

Abstract This paper deals with the problem of adaptive output feedback neural network controller design for a SISO non-affine nonlinear system. Since in practice all system states are not available in output measurement, an observer is designed to estimate these states. In comparison with the existing approaches, the current method does not require any information about the sign of control gain. In order to handle the unknown sign of the control direction, the Nussbaum-type function is utilized. In order to approximate the unknown nonlinear function, neural network is firstly exploited, and then to compensate the approximation error and external disturbance a robustifying term is employed. …

Lyapunov stabilityAdaptive controlObserver (quantum physics)Artificial neural networkComputer Networks and CommunicationsApplied MathematicsNeural network control; Observer-based control; Uncertain non-affine systems; Unknown gain direction; Control and Systems Engineering; Computer Networks and Communications; Applied Mathematics; Signal ProcessingUnknown gain directionControl engineeringNonlinear controlNonlinear systemNeural network controlExponential stabilityControl and Systems EngineeringControl theorySignal ProcessingObserver-based controlUncertain non-affine systemsMathematicsJournal of the Franklin Institute
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The chaotic Dadras–Momeni system: control and hyperchaotification

2015

In this paper a novel three-dimensional autonomous chaotic system, the so called Dadras-Momeni system, is considered and two different control techniques are employed to realize chaos control and chaos synchronization. Firstly, the optimal control of the chaotic system is discussed and an open loop feedback controller is proposed to stabilize the system states to one of the system equilibria, minimizing the cost function by virtue of the Pontryagin’s minimum principle. Then, an adaptive control law and an update rule for uncertain parameters, based on Lyapunov stability theory, are designed both to drive the system trajectories to an equilibrium or to realize a complete synchronization of t…

Lyapunov stabilityControl and OptimizationAdaptive controlApplied MathematicsSynchronization of chaosChaoticOpen-loop controllerOptimal control01 natural sciences010305 fluids & plasmasNonlinear Sciences::Chaotic DynamicsControl and Systems EngineeringControl theoryoptimal control synchronization Lyaponuv function Pontryagin minimum principle multi-scroll chaotic attractor hyperchaotic system0103 physical sciencesAttractor010301 acousticsMathematicsIMA Journal of Mathematical Control and Information
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Chaos synchronization for a class of chaotic systems via H<inf>∞</inf> control technique

2013

In this paper, the robust synchronization control for a class of chaotic systems is studied. Based on linear matrix inequality techniques and Lyapunov stability theory, a novel H∝ robust synchronization controller is designed for the possible application in real engineering. Finally, some numerical simulations are included to demonstrate the effectiveness of the proposed techniques.

Lyapunov stabilityLyapunov functionsymbols.namesakeComputer simulationRobustness (computer science)Control theorySynchronization of chaosLinear matrix inequalitysymbolsRobust controlSynchronizationMathematics2013 9th Asian Control Conference (ASCC)
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