A universal servomechanism for a class of nonlinear planar systems
type: Item
instance of: scholarly article
title: A universal servomechanism for a class of nonlinear planar systems
zbMATH Open document ID: 0863.93043
DOI: 10.1016/0096-3003(96)00011-2
author: E. P. Ryan
published in: Applied Mathematics and Computation
publication date: 1997-06-03T00:00:00Z
review text: This paper considers a direct adaptive control methodology that extends existing results on universal stabilization to universal output tracking for a specific class of second-order systems. Specifically, the paper considers the class \(L_\delta\) of uncertain single-input, single-output systems of the form \[ \ddot y(t) = a\dot y(t) + \widehat f \bigl(t,y (t)\bigr) + bu (t) \] where \(a< - \delta\), \(\delta >0\), \(b\neq 0\), and \(f(\cdot)\) is a \(C^1\) function that satisfies a type of Lipschitz condition. Also defined is the class of reference signals, given as the Sobolev space \(R = W^{3,\infty}\), which is equivalent to those functions in \(L^\infty\) whose derivatives up to order three exist and are also \(L^\infty\). Assuming that the reference signal \(r(t) \in R\) and the output \(y(t)\) generated by a system in \(L_\delta\) are both available for feedback, the paper presents the construction of an adaptive discontinuous feedback controller that results in an asymptotic tracking error that goes to zero for any reference in \(R\) and any system in \(L_\delta\). An example is presented in which the desired reference being generated is the output signal of the Lorenz equations and the system to be controlled is the Duffing equation.
reviewed by: Kevin L. Moore
Mathematics Subject Classification ID: 93C40
zbMATH DE Number: 932150
zbMATH Keywords: direct adaptive control
zbMATH Keywords: universal output tracking
zbMATH Keywords: discontinuous feedback
MaRDI profile type: Publication
full work available at URL: 0096-3003(96)00011-2
OpenAlex ID: W2136607953
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description: scientific article; zbMATH DE number 932150