On convexity of reachable sets of second order differential inclusions

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.

KEYWORDS:

• Cauchy
• Hamiltonian
• reachable set
• integral funnel
• second-order differential inclusion

2010 Mathematics Subject Classifications:

• 49K15
• 34A60
• 26E25
• 49J53

Acknowledgements

The author would like to express his sincere gratitude to the Editor-in-Chief of the Journal Applicable Analysis and anonymous reviewers for their valuable suggestions that improved the final manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).