Near Optimal Strategy for Nonlinear Stochastic Differential Games Based on the Technique of Statistical Linearization

A novel solution for a class of nonlinear zero-sum stochastic differential games is given based on the technique of statistical linearization. The near optimal feedback strategies are derived by solving the statistical state dependent Riccati equation, which is significantly different from the Riccati equation of linear systems. The case of strategy with bound limitation is also investigated. An example is given to illustrate the application of the theory.