An asymptotic scaling analysis of LQ performance for an approximate adaptive control design
type: Item
instance of: scholarly article
title: An asymptotic scaling analysis of LQ performance for an approximate adaptive control design
zbMATH Open document ID: 1009.93045
author: R. Smith
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 2003-04-27T00:00:00Z
full work available at URL: csmcfetar mcss2002.pdf
review text: The paper studies the adaptive tracking problem for a chain of integrators, where the uncertainty is static and functional. The uncertainty is specified by \(L^2/L^\infty\) or weighted \(L^2/L^\infty\) norm bounds. A standard Lyapunov-based adaptive design is analyzed, which utilizes a function approximator to induce a parametric uncertainty, on which the adaptive design is completed. Performance is measured by a modified LQ cost functional, penalizing both the tracking error transient and the control effort. With such a cost functional, it is shown that a standard control design has divergent performance when the resolution of a ``mono-resolution'' approximator is increased. A geneal construction of a class of approximators and their associated controllers, which have a uniformly bounded performance independent of the resolution of the approximator, is given.
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93B51
zbMATH DE Number: 1784734
zbMATH Keywords: adaptive tracking
zbMATH Keywords: function approximator
zbMATH Keywords: modified LQ cost functional
zbMATH Keywords: uniformly bounded performance
reviewed by: Ryszard Gessing
MaRDI profile type: Publication
OpenAlex ID: W2092119862
DOI: 10.1007/S004980200006
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description: scientific article; zbMATH DE number 1784734