A weak regularity theorem for real analytic optimal control problems
type: Item
instance of: scholarly article
title: A weak regularity theorem for real analytic optimal control problems
zbMATH Open document ID: 0638.49018
DOI: 10.4171/RMI/35
published in: Revista Matemática Iberoamericana
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/39330
review text: The following question is addressed: Given a control system of the form \(x'=f(x)+ug(x)\), -1\(\leq u\leq 1\) on a real analytic manifold M, let us assume the existence of a measurable control function u(t) defined on the interval [0,T] which steers an initial point \(x_ 1\) to a final point \(x_ 2\). Does there exist another control v(t) defined on the interval [0,T] which steers \(x_ 1\) to \(x_ 2\) and belongs to some prescribed subclass \({\mathcal R}\) of control functions? It is proved by an example that the answer is no if f and g are \(C^{\infty}\) vector fields. However, if the system is real analytic and \({\mathcal R}\) consists of functions which are analytic on an open dense subset of [0,T], the answer is yes.
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 57R27
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93B03
zbMATH DE Number: 4040685
zbMATH Keywords: nonlinear systems
zbMATH Keywords: real analytic manifold
author: Héctor J. Sussmann
reviewed by: Andrea Bacciotti
MaRDI profile type: Publication
OpenAlex ID: W1971238785
description: scientific article; zbMATH DE number 4040685