Policy-Iteration-Based Asynchronous Control of Jump Systems With Hidden Mode Observation and <i>H</i> _∞ Disturbance Attenuation

This article is concerned with the asynchronous $H_{\infty }$ control design based on model-free policy iteration (PI) algorithm for a class of discrete-time hidden Markov jump system, where a hidden Markov model is developed to characterize the asynchronous phenomenon between the controller modes and the system modes. A pair of zero-sum asynchronous control and disturbance strategies are constructed to achieve a tradeoff between value function and control performance. The presented approach shows two pivotal aspects: 1) the asynchronous PI algorithm is not dependent on strict temporal alignment between the controller and the system's dynamics, enhancing flexibility of the control scheme and 2) it relies on the collected data to solve the algebraic Reccati equation iteratively, which avoids the need for system-internal and transfer probability information, and circumvents the interference of coupled terms. Subsequently, it is verified that the designed PI algorithm monotonically converges to an optimal solution and the system based on this optimal solution is stochastically stable in the mean-square sense. Finally, the effectiveness of this approach is validated by conducting a simulation experiment on a DC motor device system.