Study of a Warfare Differential Game via Dynamic Programming Approach

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.