Adaptive critic control with multi‐step policy evaluation for nonlinear zero‐sum games

Abstract

To attenuate the effect of disturbances on control performance, a multi‐step adaptive critic control (MsACC) framework is developed to solve zero‐sum games for discrete‐time nonlinear systems. The MsACC algorithm utilizes multi‐step policy evaluation to obtain the solution of the Hamilton–Jacobi–Isaac equation, which is faster than that of the one‐step policy evaluation. The convergence rate of the MsACC algorithm is adjustable by varying the step size of the policy evaluation. In addition, the stability and convergence of the MsACC algorithm are proved under certain conditions. In order to realize the MsACC algorithm, three neural networks are established to approximate the control input, the disturbance input, and the cost function, respectively. Finally, the effectiveness of the MsACC algorithm is verified by two simulation examples, including a linear system and a nonlinear plant.