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In this paper, a new method is proposed to compute the rolling Nashequilibrium of the time-invariant nonlinear two-person zero-sum differentialgames. The idea is to discretize the time to transform a differential game intoa sequential game with several steps, and by introducing state-value function,transform the sequential game into a recursion consisting of severalnormal-form games, finally, each normal-form game is solved with actionabstraction and regret matching. To improve the real-time property of theproposed method, the state-value function can be kept in memory. This methodcan deal with the situations that the saddle point exists or does not exist,and the analysises of the existence of the saddle point can be avoided. If thesaddle point does not exist, the mixed optimal control pair can be obtained. Atthe end of this paper, some examples are taken to illustrate the validity ofthe proposed method.

Recursive Regret Matching: A General Method for Solving Time-invariant Nonlinear Zero-sum Differential Games