Study of a Warfare Differential Game via Dynamic Programming Approach

Touffik Bouremani () and Yacine Slimani ()
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Touffik Bouremani: Ferhat Abbas University Setif 1
Yacine Slimani: Ferhat Abbas University Setif 1

Dynamic Games and Applications, 2024, vol. 14, issue 4, No 1, 733-750

Abstract: Abstract We use some recent developments in dynamics programming method to obtain the complete and theoretically justified solution of a differential game formulated and studied in Chen and Qiu (Abstr Appl Anal 2014:1–8, 2014. https://doi.org/10.1155/2014/837431 ) using the Lanchester equation. We use a certain refinement of Cauchy’s method of characteristics for stratified Hamilton–Jacobi equations to describe a large set of admissible trajectories and identify a domain on which the value function exists and is generated by a pair of admissible feedback strategies. Its optimality is justified by using one of the well-known verification theorems as an argument for sufficient optimality conditions.

Keywords: Differential game; Differential inclusion; Feedback strategies; Dynamic programming; Hamiltonian flow; Value function; Verification theorem; 49N70; 49N35; 49N90; 91A23; 49L20; 34A60 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13235-023-00523-w

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