Data-based Optimal Control for Discrete-time Zero-sum Games of 2-D Systems Using Adaptive Critic Designs

In this paper, an iterative adaptive critic design (ACD) algorithm is proposed to solve a class of discrete-time two-person zero-sum games for Roesser type 2-D system. The idea is to use adaptive critic technique to obtain the optimal control pair iteratively to make the performance index function reach the saddle point of the zero-sum games. The proposed iterative ACD algorithm can be implemented based on the input and state data without the system model. Stability analysis of the 2-D system is presented and the convergence property of the performance index function is also proved. Neural networks are used to approximate the performance index function and compute the optimal control policies, respectively, for facilitating the implementation of the iterative ACD algorithm. The optimal control scheme of the air drying process is given to illustrate the performance of the proposed method.