Adaptive control systems with augmented errors
type: Item
instance of: scholarly article
title: Adaptive control systems with augmented errors
zbMATH Open document ID: 0857.93053
published in: Automation and Remote Control
publication date: 1997-03-16T00:00:00Z
review text: A survey on the following problem is presented. Consider the class of time-invariant, linear, single-input single-output systems \[ A\bigl({\textstyle{d\over dt}}\bigr)y(t)=k B\bigl( {\textstyle{d\over dt}}\bigr)u(t), \] where \(A(\cdot)\) and \(B(\cdot)\) are monic polynomials with real coefficients and \({d\over dt}\) denotes the usual differential operator. The coefficients of the polynomials are unknown, the only assumptions made are: \(B(s)\) is Hurwitz, \(k\) is positive, and the degrees of the polynomials \(A(s)\) and \(B(s)\) are known. The control objective is to find an adpative controller such that \(y(t)-y_m(t)\) tends to 0 as \(t\to\infty\). Here \(y_m(t)\) denotes the output of the reference model \[ A_m\bigl({\textstyle{d\over dt}}\bigr)y_m(t)= k_mB_m\bigl({\textstyle{d\over dt}}\bigr)u(t), \] where \(A_m(\cdot)\) and \(B_m(\cdot)\) are monic polynomials with the same degree as \(A\) and \(B\). Attention is given to the augmentation of the tracking error and improvements of identification properties and the rate of convergence of adaptation algorithms.
reviewed by: Achim Ilchmann
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93-02
zbMATH DE Number: 922170
zbMATH Keywords: adaptive stabilization
zbMATH Keywords: survey
zbMATH Keywords: adpative controller
zbMATH Keywords: tracking error
author: V. O. Nikiforov
author: Alexander Fradkov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 922170