Non-identifier-based high-gain adaptive control
type: Item
instance of: scholarly article
title: Non-identifier-based high-gain adaptive control
zbMATH Open document ID: 0786.93059
published in: Lecture Notes in Control and Information Sciences
publication date: 1993-11-22T00:00:00Z
review text: Adaptive control without plant identification is sometimes referred to as universal adaptive control. In order to define what universal adaptive control is, let \({\mathfrak P}\) be a set of plants with \(m\) inputs \((u_ 1,\dots,u_ m)^ T= u\) and \(p\) outputs \((y_ 1,\dots,y_ p)^ T= y\). Usually, each element in \({\mathfrak P}\) is given by a controlled and observed ordinary differential equation. A single control law of the form \[ u(t)= f(t,k(t),y(t)),\quad\dot k(t)= g(t,k(t),y(t)),\quad k(t_ 0)\in\mathbb{R}^{\ell} \] is a \({\mathfrak P}\)-universal adaptive controller if it guarantees that every plant in \({\mathfrak P}\) exhibits some prescribed dynamic behaviour (for example, attractivity or stability of an equilibrium or asymptotic output tracking of some reference signal). The book gives a rather complete account of the state of the art of universal adaptive control for classes \(\mathfrak P\) of linear systems which are stabilizable by high-gain static output feedback. The assumption of high-gain stabilizability implies that the systems under consideration are necessarily minimum-phase and of relative degree \(\leq 2\). However, no assumptions on the McMillan degree of the system are imposed. The book contains 8 chapters, of which the first one is of an introductory nature-illustrating the problems under consideration by a simple example and outlining the contents of the book. Chapters 2 and 3 do not deal with the adaptive control problem, but contain a number of results on minimum-phase, high-gain stabilizable and almost strictly positive real systems which are needed in the rest of the book. In Chapter 4 the author studies the adaptive stabilization problem and presents a number of adaptive high-gain stabilization schemes for minimum-phase systems of relative degree 1. Moreover, stabilization results for systems of relative degree 1 or 2 and for systems with non- zero feedthrough are given. Chapter 5 is devoted to the adaptive tracking problem. Results…
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93D30
Mathematics Subject Classification ID: 93-02
zbMATH DE Number: 462639
zbMATH Keywords: universal adaptive controller
zbMATH Keywords: closed-loop system
author: Achim Ilchmann
reviewed by: H. Logemann
MaRDI profile type: Publication
DOI: 10.1007/BFB0032266
description: scientific article; zbMATH DE number 462639