High-order necessary conditions of optimality for nonlinear control systems
type: Item
instance of: scholarly article
title: High-order necessary conditions of optimality for nonlinear control systems
zbMATH Open document ID: 0732.49013
DOI: 10.1016/0167-6911(91)90058-M
author: Andrej V. Sarychev
published in: Systems \& Control Letters
publication date: 1991-01-01T00:00:00Z
review text: Consider the control system \(\dot x=f_{\tau}(x)+g(x)\cdot u\), where \(f_{\tau}\) is a time-dependent vector field on a manifold \(M\), \(g=(g_1,\ldots,g_r)\) a collection of vector fields on \(M\) and \(u=(u_1,\ldots,u_r)\) a vector valued function of the time parameter. The main result of the paper under review is a set of necessary conditions for time-optimality of solutions in terms of the Lie brackets of the \(g_j\)'s. More precisely, the author first gives a Pontryagin type maximum principle and then uses a Hall-basis of the free Lie algebra in \(r\) indeterminates to rewrite the conditions including the variational cone as a condition involving the Lie brackets.
reviewed by: Joachim Hilgert
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 4210920
zbMATH Keywords: time-dependent vector field
zbMATH Keywords: necessary conditions for time-optimality
zbMATH Keywords: Lie brackets
zbMATH Keywords: Pontryagin type maximum principle
zbMATH Keywords: Hall-basis
zbMATH Keywords: variational cone
MaRDI profile type: Publication
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full work available at URL: 0167-6911(91)90058-m
OpenAlex ID: W2074567562
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description: scientific article; zbMATH DE number 4210920