Suboptimal Approximation Approach of Nash Equilibrium Strategy for two-Person Nonlinear-Quadratic Differential Game

摘要

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