The Suboptimal Nash Equilibrium Strategy For Two-person Continuous Nonlinear-quadratic Differential Game

This paper deals with a class of Nash equilibrium strategy problems for two-person continuous nonlinear-quadratic dynamic game. A successive approximation approach (SAA) is presented. By using SAA, the nonlinear system Nash equilibrium problem is transformed into a sequence of special non-homogeneous linear two-point boundary value (TPBV). The finite-step iteration manner of the Nash equilibrium strategy is derived, and the uniformity and absolutization of the algorithm's convergence has been proved.