Global null controllability of nonlinear delay equations with controls in a compact set
type: Item
instance of: scholarly article
title: Global null controllability of nonlinear delay equations with controls in a compact set
zbMATH Open document ID: 0594.93014
DOI: 10.1007/BF00938816
published in: Journal of Optimization Theory and Applications
publication date: 1987-01-01T00:00:00Z
review text: The question of controlling some nonlinear retarded functional differential equations from an initial function to the zero function is considered. The control sets M(\(\Omega)\) are square integrable functions with values in the unit closed sphere \(L_ 2([t_ 0,\infty),E^ m)\) with center the origin. Assuming that the linear approximation of the nonlinear equation is null controllable with some integrable controls on some interval \([t_ 0,t_ 1-2r]\), where \(t_ 0\) is sufficiently large and where \(r>0\) is the delay, and assuming that the nonlinear system, with \(u=0\), is uniformly globally asymptotically stable, we show that the nonlinear control process is globally null controllable with controls \(u\in M(\Omega)\). The paper gives conditions which guarantee the stability assumptions, and also indicates conditions which yield the null controllability assumptions of the linear approximation. Our research extends known results on ordinary differential processes.
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 3956897
zbMATH Keywords: nonlinear retarded functional differential equations
zbMATH Keywords: null controllability
zbMATH Keywords: linear approximation
zbMATH Keywords: uniform asymptotic stability
author: Ethelbert Nwakuche Chukwu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3956897