Differential Dynamic Programming for Finite-Horizon Multi-Player Non-Zero-Sum Differential Games of Nonlinear Systems

Abstract

In this paper, an iterative algorithm based on differential dynamic programming (DDP) is developed to solve the finite-horizon multi-player non-zero-sum (NZS) games. By using the DDP, the coupled Hamilton-Jacobi (HJ) equations are expanded from partial differential forms to higher-order differential forms. By approximating the value functions and optimal control policies through several finite sets of basis functions, the DDP expansions are transformed into algebraic matrix equations in integral forms. Then a policy iteration (PI) algorithm is provided to solve the feedback Nash equilibrium of above NZS games. Finally, two simulation examples are given to demonstrate the feasibility of the developed algorithm.