Linear Quadratic Pursuit–Evasion Games on Time Scales

Davis Funk, Richard Williams and Nick Wintz ()
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Davis Funk: Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095, USA
Richard Williams: Department of Mathematics and Physics, Marshall University, Huntington, WV 25755, USA
Nick Wintz: Department of Mathematics and Statistics, Radford University, Radford, VA 24142, USA

Mathematics, 2025, vol. 13, issue 20, 1-20

Abstract: In this paper, we unify and extend the linear quadratic pursuit–evasion games to dynamic equations on time scales. A mixed strategy for a single pursuer and evader is studied in two settings. In the open-loop setting, the corresponding controls are expressed in terms of a zero-input difference. In the closed-loop setting, the corresponding controls require a mixing feedback term when rewriting the system in extended state form. Finally, we offer a numerical simulation.

Keywords: dynamic equations on time scales; optimal control; pursuit–evasion games; Riccati equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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