Nonzero-sum differential games of continuous-Time nonlinear systems with uniformly ultimately ε-bounded by adaptive dynamic programming

In this paper, a single network adaptive dynamic programming (ADP) control method is presented to obtain the nearly optimal control policies for the non-zero sum (NZS) differential game problem of the autonomous nonlinear system. The Osgood condition, instead of the traditional Lipschitz condition, is firstly introduced to policy iteration to guarantee the existence and uniqueness of the solution of the dynamic nonlinear systems and to weaken the limited conditions of nonlinear dynamic functions f ( x ), g ( x ) and k ( x ). Moreover, this adaptive control pattern finds in real-time approximations of the optimal value and the non-zero sum Nash-equilibrium, while also ensuring the uniform ultimate ε-boundedness of the closed-loop system. Further, as the number of hidden-layer neurons tends to infinite, the approximation errors converge to zero. As a result, the closed-loop system is asymptotically stable. Finally, the effectiveness of the proposed near-optimal control pattern is verified by a simulation example.