Contribution of the dynamic programming method to solving the d'orchestre differential game.

Abstract

In this thesis, we focus on applying St. Mirică's Dynamic Programming method to solve the differential game introduced by R. Isaacs. We propose feedback strategies as a new contribution that offers adaptability, efficiency, and simplicity while reducing algorithmic complexity. This approach employs a refined Cauchy characteristics method to handle stratified Hamilton-Jacobi equations while ensuring the existence of the value function. The optimality of the feedback strategies is rigorously validated using the Verification Theorem for locally Lipschitz value functions and further supported by established numerical tests.