On the regularity of optimal controls
type: Item
instance of: scholarly article
title: On the regularity of optimal controls
zbMATH Open document ID: 0636.49009
DOI: 10.1007/BF00945414
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1987-01-01T00:00:00Z
review text: The authors show that regularity proofs for closed-loop optimal controls require results on piecewise regularity with bounds on the number of switchings for open-loop optimal controls. They survey known results of this kind [\textit{A. Bressan}, SIAM J. Control Optimization 23, 38-48 (1985; Zbl 0557.49011); the second author, J. Differ. Equations 31, 31-52 (1979; Zbl 0407.93010) and ibid. 25, 433-465 (1987)] and announce new ones for the time-optimal control problem for systems of type \[ \Sigma: \dot x=f(x)+g(x)u,\quad | u| \leq 1,\quad x\in R^ n,\quad n=2,3. \] The results are obtained by characterizing the local structure of time-optimal trajectories near a reference point p through the Lie bracket configuration at p of the family of vector fields generated by \(\Sigma\).
Mathematics Subject Classification ID: 49K30
Mathematics Subject Classification ID: 93B99
Mathematics Subject Classification ID: 57R27
Mathematics Subject Classification ID: 93B27
Mathematics Subject Classification ID: 17B99
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 4036572
zbMATH Keywords: regularity
zbMATH Keywords: time-optimal control problem
zbMATH Keywords: Lie bracket
author: Heinz Schättler
author: Héctor J. Sussmann
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00945414
OpenAlex ID: W1528649503
description: scientific article; zbMATH DE number 4036572