On convexity of reachable sets of second order differential inclusions

Mahmudov E.

APPLICABLE ANALYSIS, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1080/00036811.2022.2149507
  • Journal Name: APPLICABLE ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Cauchy, Hamiltonian, reachable set, integral funnel, second-order differential inclusion, ATTAINABLE SET, OPTIMIZATION, DISCRETE, EQUATIONS, APPROXIMATION, DUALITY
  • Istanbul Technical University Affiliated: Yes

Abstract

In control theory, there is growing interest in the evolution of sets, especially integral funnels and reachable sets at a certain time. In this paper, we establish sufficient conditions for the convexity of reachable sets for an object whose behavior is described by the second-order differential inclusions. This fact is proved using the concavity of the Hamilton function in the first argument. Further, in connection with the usefulness of the Hamilton function, some of its properties, such as continuity and Lipschitz property, are investigated. At the end of the article, the results obtained are demonstrated with some examples.