A Baire Category Approach to the Bang-Bang Property

Alberto Bressan, Benedetto Piccoli

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Abstract

The aim of this paper is to develop a new technique, based on the Baire category theorem, in order to establish the closedness of reachable sets and the existence of optimal trajectories for control systems, without the usual convexity assumptions. The bang-bang property is proved for a new class of "concave" multifunctions, characterized by the existence of suitable linear selections. The proofs rely on Lyapunov’s theorem in connection with a Baire category argument.

Original languageEnglish (US)
Pages (from-to)318-337
Number of pages20
JournalJournal of Differential Equations
Volume116
Issue number2
DOIs
Publication statusPublished - Mar 1 1995

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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