${H_\infty }$ Consensus for Discrete-Time Fractional-Order Multi-Agent Systems With Disturbance via Q-Learning in Zero-Sum Games

This paper investigates $H_\infty$ consensus problem for discrete-time fractional-order multi-agent systems (DTFOMASs) with external disturbance in both state and output feedback controls. Based on the short-memory principle, the original DTFOMASs are transformed into classical discrete-time systems. Then, two consensus protocols with finite-dimensional memory for state and output feedback are proposed. By using the Bellman equation approach and recursive least-squares, two Q-learning (QL) algorithms for two-player zero-sum games (ZSG) to $H_\infty$ control are presented to learn the optimal feedback gain matrices without any information from the system dynamics and network topology. Furthermore, the DTFOMASs with external disturbance can achieve $H_\infty$ state and output consensus under the two proposed protocols, respectively. In the end, two real scenarios of high-speed train running on the railway section of “Zhengzhou-Wuhan” are applied to check the validity of the proposed approaches.