Influence Function Based Off-policy Q-learning Control for Markov Jump Systems

This paper presents an off-policy Q-learning approach based on influence function for addressing H∞ control of Markov jump systems. Unlike existing literatures, the mode classification and parallel update method is developed to directly decouple the relationship among matrices across different modes, tackling the most challenging aspect of this issue. Subsequently, we utilize the off-policy algorithm to derive the optimal policy, which allows for efficient learning without the need to follow the current policy being improved. This approach is particularly advantageous as it enables the algorithm to explore and evaluate different policies from historical data, thus circumventing the limitations associated with specific forms of disturbance updates. Moreover, the influence function is employed for data cleansing during the learning process, thereby enabling a more efficient learning period. A numerical example and a DC motor model are presented to illustrate the validity of the proposed method.