  In this paper, a new method is proposed to compute the rolling Nash
equilibrium of the time-invariant nonlinear two-person zero-sum differential
games. The idea is to discretize the time to transform a differential game into
a sequential game with several steps, and by introducing state-value function,
transform the sequential game into a recursion consisting of several
normal-form games, finally, each normal-form game is solved with action
abstraction and regret matching. To improve the real-time property of the
proposed method, the state-value function can be kept in memory. This method
can 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 the
saddle point does not exist, the mixed optimal control pair can be obtained. At
the end of this paper, some examples are taken to illustrate the validity of
the proposed method.
