Data-driven Differential Games for Affine Nonlinear Systems

This paper presents a data-driven optimal approach based on differential dynamic programming (DDP) for two-person differential game of nonlinear affine systems. Using test data, the Hamilton-Jacobi-Isaacs (HJI) equation is expanded into a set of high-order differential equations. Basis functions is adopted to approximate the unknown system function and value function. Based on the approximation, a data-driven optimal approach is proposed to obtain the unknown coefficients of the basis functions. A numerical example is proposed to demonstrate the effectiveness of this method.