A note on convexity in smooth nonlinear systems
type: Item
instance of: scholarly article
title: A note on convexity in smooth nonlinear systems
zbMATH Open document ID: 0971.49001
DOI: 10.1007/BF02673837
author: S. A. Vakhrameev
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-11-07T00:00:00Z
review text: The paper presents an existence theorem for a two-point time-optimal control problem associated with a smooth control system \({\dot x}=f(x,u)\), \(x \in M\), \(u \in U\), where \(M\) is an \(n\)-dimensional \(C^{\infty}\)-manifold that is regularly embedded into \(R^d\); \(U\) is a compact convex polyhedron in \(R^m\); \(\{ f(\cdot,u): u \in R^m \}\) is a family of \(C^{\infty}\) vector fields on \(M\) that smoothly depend on \(u\). The result completes a previous bang-bang theorem by the author which states the bang-bang structure of the solution for this problem provided that the optimal control exists.
Mathematics Subject Classification ID: 49J15
zbMATH DE Number: 1526514
zbMATH Keywords: time-optimal control problem
zbMATH Keywords: existence theory
zbMATH Keywords: convexity
zbMATH Keywords: bilinear systems
zbMATH Keywords: matrix exponent
reviewed by: Mikhail Yu. Kokurin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1526514