A robust indirect discrete adaptive-control approach based on passitivity results for nonlinear systems
type: Item
instance of: scholarly article
title: A robust indirect discrete adaptive-control approach based on passitivity results for nonlinear systems
zbMATH Open document ID: 0663.93044
DOI: 10.1016/0898-1221(88)90160-5
publication date: 1988-01-01T00:00:00Z
review text: This paper considers the problem of designing a robust adaptive algorithm for discrete systems. This algorithm employs the usual method of an on- line adjustment of the gain matrix so as to reduce the error signal to zero, while other signals remain bounded. It is well known that usually the adaptive systems present problems and thus the theoretical results fail. The problems are due to poor transient performances and poor behaviour which implies instability under unmodelled dynamics. In this paper the problem of instability is treated as a robustness problem, so as to make the closed-loop system stable under variations of the parameters. A passitivity result taken from \textit{C. A. Desoer} and \textit{M. Vidyasagar} [Feedback systems: Input-output properties (1975; Zbl 0327.93009)] is used to formulate a global convergence criterion in terms of positive realness of a transfer matrix. The main result is presented in Theorem 3.2 in the text of the paper. The robustness is provided in terms of the strictly discrete positive realness of a marix termed \(W(z)Gv(z)\) which is easily computable. It is noted that the results are valid for any initial conditions of the adaptive algorithm. Basically, the results in this paper extend the work by \textit{M. A. L. Thathachar} and \textit{F. Gajendran} [Int. J. Control 34, 127--142 (1981; Zbl 0467.93045)] in the case that additive noise is present (together with unmodelled dynamics) while stability is maintained for the closed- loop adaptive system.
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93D25
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 4085531
zbMATH Keywords: robust adaptive algorithm
zbMATH Keywords: unmodelled dynamics
zbMATH Keywords: robustness
zbMATH Keywords: passitivity
zbMATH Keywords: strictly discrete positive realness
Wikidata QID: Q57675888
author: M. De la Sen
reviewed by: M. A. Christodoulou
MaRDI profile type: Publication
full work available at URL: 0898-1221(88)90160-5
OpenAlex ID: W2137373850
cites work: A structural principle for a class of adaptive systems
cites work: Model reference adaptive control with an augmented error signal
cites work: Stable adaptive controller design, part II: Proof of stability
cites work: Adaptive sampling for improving the adaptation transients in hybrid adaptive control
cites work: Suboptimization techniques for improving transients in adaptive control†
cites work: Application of numerical methods to the acceleration of the convergence of the adaptive control algorithms
cites work: Adaptive systems with reduced models
cites work: A robust indirect adaptive-control approach
cites work: Q4093255
cites work: A global convergence criterion for discrete-time multivariable adaptive systems
cites work: Q4401837
cites work: Q5180741
cites work: Q5657947
Recommended article: Robust discrete-time simple adaptive regulation
Recommended article: Closed-loop identification for the best asymptotic performance of adaptive robust control
Recommended article: Robust adaptive stabilization of discrete-time first-order systems
Recommended article: On the robustness of adaptive controllers using relative deadzones
Recommended article: An input-output view of robustness in adaptive control
Recommended article: Adaptive regulator for discrete-time nonlinear nonparametric systems
Recommended article: Unmodeled dynamics in adaptive control systems revisited
Recommended article: Q3140708
Recommended article: Global and local stability properties of a non-SPR output error estimator
Recommended article: Q3975411
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4085531