Iteration algorithm for solving the optimal strategies of a class of nonaffine nonlinear quadratic zero-sum games

A iteration algorithm is derived to solve the optimal strategies of continuous-time nonaffine nonlinear quadratic zero-sum game in this paper. The nonaffine nonlinear quadratic zero-sum game is transformed into an equivalent sequence of linear quadratic zero-sum games. The associated Hamiltion-Jacobi-Isaacs (HJI) equation is transformed into a sequence of algebraic Riccati equations. The optimal strategies of the zero-sum game are obtained by iteration. The convergence of the iteration algorithm is proved under very mild conditions of local Lipschitz continuity. Finally, this approach is applied to a numerical example to demonstrate its convergence and effectiveness.