Nonlinear Adaptive Control: Regulation-Tracking-Oscillations

Fradkov, Alexander L.

doi:10.1016/b978-0-08-042367-8.50072-0

Cited by 6 publications

(10 citation statements)

References 34 publications

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“…Another related idea is passification by means of shunting introduced by Fradkov [28]. All these approaches represent derivation of a loop-transfer function with SPR properties for a control object without SPR properties by means of dynamic extensions or observers.…”

Section: Discussionmentioning

confidence: 99%

Observer-based strict positive real (SPR) switching output feedback control

Johansson

Robertsson

Shiriaev

2004

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)

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This paper considers switching output feedback control of linear systems and variablestructure systems. Theory for stability analysis and design for a class of observer-based feedback control systems is presented. It is shown how a circlecriterion approach can be used to design an observerbased state feedback control which yields a closedloop system with specified robustness characteristics. The approach is relevant for variable structure system design with preservation of stability when switching feedback control or sliding mode control is introduced in the feedback loop. It is shown that there exists a Lyapunov function valid over the total operating range and this Lyapunov function has also interpretation as a storage function of passivity-based control and a value function of an optimal control problem. The Lyapunov function can be found by solving a Lyapunov equation. Important applications are to be found in hybrid systems with switching control and variable structure systems with high robustness requirements.

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Section: Discussionmentioning

confidence: 99%

Observer-based strict positive real (SPR) switching output feedback control

Johansson

Robertsson

Shiriaev

2004

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)

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“…This more complicated problem, which corresponds to the real situations, will be referred to as one of adaptive synchronization [4], [6], [7], [15]. This paper gives the brief exposition of the recent results on adaptive synchronization of chaotic systems obtained by the so called speed-gradient (SG) method [4], [8].…”

Section: Introductionmentioning

confidence: 99%

Adaptive synchronization of chaotic systems based on speed gradient method and passification

Fradkov

Markov

1997

IEEE Trans. Circuits Syst. I

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107

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A problem of synchronizing two nonlinear multidimensional systems with unknown parameters is considered. Two general procedures for adaptive synchronization law design based on speed-gradient method are proposed. Conditions ensuring the synchronization are given. The second procedure is based on passification of error system (making it passive by feedback). The results are illustrated by examples: synchronizing a pair of Chua's circuits and a pair of circuits with tunnel diodes. Computer simulation results confirming theoretical analysis are given.

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“…Control of oscillatory systems requires achieving nonclassical control goals (swinging, synchronization) as well as describing and analyzing complex motions of the closed loop system. A new approach to stabilization of a desired level of oscillations for Hamiltonian systems based on the speed}gradient method (Fradkov, 1979) and energy objective functions was proposed in Fradkov, (1994Fradkov, ( , 1996, Fradkov, Guzenko, Hill and Pogromsky, (1995) and Fradkov, Makarov, Shiriaev and Tomchina, (1997). Recently, it was extended to a class of nonlinear systems, see Shiriaev, (2000a,b).…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

Stabilization of invariant sets for nonlinear non-affine systems

Shiriaev

Fradkov

2000

Automatica

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The problem of the global and local stabilization of invariant sets for general nonlinear controlled systems is considered. New state feedback stabilizing controllers and su$cient conditions of asymptotic stability of a goal set with the speci"ed region of attraction are proposed. The proofs of the obtained results are based on the detailed analysis of the -limit sets of the closed-loop system with the speed}gradient (or`Jurdjevic}Quinna) controllers for`a$nizeda controlled system. Two illustrating examples are given.

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Nonlinear Adaptive Control: Regulation-Tracking-Oscillations

Cited by 6 publications

References 34 publications

Observer-based strict positive real (SPR) switching output feedback control

Observer-based strict positive real (SPR) switching output feedback control

Adaptive synchronization of chaotic systems based on speed gradient method and passification

Stabilization of invariant sets for nonlinear non-affine systems

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