Study of a warfare differential game via dynamic programming approach

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 \cite{CHE} 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 of one of the well-known verification theorems as an argument for sufficient optimality conditions. MSC Classification: 49N70 , 49N35 , 49N90 , 91A23 , 49L20 , 34A60