Intelligent Constrained Zero-Sum Game Design With Advanced Critic Learning Including a Two-Area Power System Application

In this article, an advanced critic learning technique is established to handle the continuous-time (CT) multiplayer zero-sum game (MZSG) problem with asymmetric constraints. To begin with, a novel asymmetric constraint algorithm is presented, which relaxes the restrictions on the control matrices compared to prior related studies. Ulteriorly, the Hamilton-Jacobi-Isaacs equation, the optimal controls, and the worst disturbances are deduced for asymmetric constrained MZSGs (ACMZSGs). Since the acquired Hamilton-Jacobi-Isaacs equation is intractable to solve, an advanced critic learning scheme is built to attain the approximations of the optimal controls and the worst disturbances. It is noteworthy that this article develops a new weight tuning rule to lower the need for the initial admissible controls. Immediately after that, the stability analysis of the control system is given. In the end, the load frequency control problem for a two-area power system with linear dynamics is considered, and the simulation for a nonlinear system is performed to test the feasibility of the suggested control scheme. In particular, comparative experiments are established to further demonstrate the efficacy of the proposed weight tuning rule and the applicability of the proposed asymmetric constraint algorithm.