Invariant Solutions of Differential Games with Measures: A Discontinuous Time Reparameterization Approach

Elena Goncharova () and Maxim Staritsyn ()
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Elena Goncharova: Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences
Maxim Staritsyn: Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 1, No 18, 382-400

Abstract: Abstract The paper is devoted to bilevel qualitative games with impulsive dynamics described by a measure differential equation. We study games with fixed impulses, and games with impulsive control in the hands of the lower level player, provided that the upper level player aims to ensure the existence of invariant solutions to a measure differential equation under any admissible answer of the opponent. We give sufficient conditions for weak invariance of time-varying domains with respect to the impulsive dynamical games.

Keywords: Dynamic games; Measure-driven dynamical systems; Viability problems; Weak invariance; 49N25; 49N70; 91A20; 91A25 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-014-0691-7

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