Barrier-Critic Adaptive Robust Control of Nonzero-Sum Differential Games for Uncertain Nonlinear Systems With State Constraints

Abstract

In this article, for the nonzero-sum (NZS) differential games problem of uncertain nonlinear systems with state constraints, an adaptive robust stabilization scheme based on the control barrier function (CBF) is presented under the influence of random disturbances and control input matrix uncertainty. To deal with the impact of uncertainty on the system, the nominal system of the original system is adopted and the cost functions associated with each player are appropriately chosen to convert the robust regulation problem of multiplayer differential games into an optimal regulation problem. Furthermore, the purpose of combining the cost function relevant to each player with the CBF is to make the system states evolve in the safe area. Different from the classical actor–critic dual neural network (NN), each player only needs a critic NN to approach the corresponding cost function without the restriction of the initial stabilizing control. Combined with the Lyapunov stability theory, under the combined influence of random disturbances and state constraints, the state and critic NN weights of the closed-loop system are guaranteed to be uniformly ultimately bounded (UUB). Finally, two simulation examples are used to verify the validity of the presented scheme.