Adaptive control of nonlinear systems with nonlinear parameterization

Karsenti, Laurent; Lamnabhi‐Lagarrigue, Françoise; Bastin, Georges

doi:10.1016/0167-6911(95)00055-0

Cited by 39 publications

(13 citation statements)

References 7 publications

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“…This fact prevents from applying previously mentioned results. There exist a number of solutions for nonlinearly parameterized problems [5], [10], [16], [18], [19], [20], [22], [30] usually based on tuned robust feedbacks. However, they can not be applied to energy control problem due to the requirement of control law boundedness.…”

Section: Robust and Adaptive Partial Stabilization For A Class Of Nonmentioning

confidence: 99%

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Robust and Adaptive Partial Stabilization for a Class of Nonlinearly Parameterized Systems

Efimov¹,

Fradkov²

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Section: Robust and Adaptive Partial Stabilization For A Class Of Nonmentioning

confidence: 99%

“…Yd )e+p(y) -p(yd )+B(y)0-B(y )Y -K(Yd)d2(t)+R(y)d3+[R(y)-R(yd)]u+(15) +dl(t)+[A(y)-A(Yd ) ]x, 6 G(Yd ) 6 + (Y) (Yd) [ B(y) -B(Yd ) ]0 -K(Yd)d2(t)+R(y)d3+[R(y)-R(yd)]u+(16) +dl(t)+[A(y)-A(Yd ) ] xFor the case of absence of disturbances d = 0 systems (15),(16) can be rewritten as follows e G(y)e+B(y)[O0],…”

mentioning

confidence: 99%

Robust and Adaptive Partial Stabilization for a Class of Nonlinearly Parameterized Systems

Efimov¹,

Fradkov²

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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“…It is clear that to get some workable results we have to impose some additional restrictions on f. For instance, if we additionally impose the conditions of f (0, )"0, and f being twice continuously di!erentiable in x, then a Taylor expansion argument allows us to prove that the closed loop of the certainty equivalent adaptive system based on the "rst-order approximation is locally stable.S This is the case considered in Reference [12].…”

Section: Motivationmentioning

confidence: 99%

Semi‐adaptive control of convexly parametrized systems with application to temperature regulation of chemical reactors

Fradkov

Ortega

Bastin

2001

Adaptive Control & Signal

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In this paper, we are interested in the problem of adaptive control of non-linearly parametrized systems. We investigate the viability of de"ning a stabilizing parameter update law for the case when the plant model is convex on the uncertain parameters. We show that, when the only prior knowledge is convexity, there does not exist an adaptation law*derivable from the standard separable Lyapunov function technique of Parks*applicable for all the state space. Therefore, we propose a semi-adaptive state feedback controller where adaptation takes place only in the region of the state space where convexity can be used to reduce parameter uncertainty. In the remaining part of the state space we freeze the adaptation and switch to a robust controller. This scheme ensures semi-global stability for convexly parametrized non-linear systems with matched uncertainty. The proposed controller is then applied to the problem of temperature regulation of continuous stirred exothermic chemical reactors where reaction heat is convex in the uncertain parameters.

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“…This shows that the uncertainties in (1), represented by f (x p ), can not be parameterized. The adaptive tracking control of uncertain nonlinear systems has been attracted much attention during the past decades (see, for instance, [1], [2], [3], [4] and the references therein). However, most researches of the adaptive tracking control devoted to the systems with linearly parameterized uncertainties, that is, the uncertainties can be represented by functions of the form f (x p ) = θ T ψ(x p ), where ψ(x p ) is a known function vector and θ is an unknown parameter vector.…”

Section: Introductionmentioning

confidence: 99%

Model Reference Adaptive Control of a Class of Uncertain Nonlinear Systems Based on Neural Networks

Chen

2009

2009 International Conference on Artificial Intelligence and Computational Intelligence

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The paper deals with the problem of model reference adaptive control of a class of uncertain nonlinear systems by output feedback based on neural networks. The uncertainty of the system can not be parameterized and its upper bound is unknown. In order to approximate the uncertainty via neural networks, a technique of global approximation of continuous functions is introduced. Based on the technique, a method of designing adaptive tracking controllers for the systems is presented, which guarantees that all signals in the closed loop system are bounded and the tracking error converges to a desired neighborhood of zero.

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Adaptive control of nonlinear systems with nonlinear parameterization

Cited by 39 publications

References 7 publications

Robust and Adaptive Partial Stabilization for a Class of Nonlinearly Parameterized Systems

Robust and Adaptive Partial Stabilization for a Class of Nonlinearly Parameterized Systems

Semi‐adaptive control of convexly parametrized systems with application to temperature regulation of chemical reactors

Model Reference Adaptive Control of a Class of Uncertain Nonlinear Systems Based on Neural Networks

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