Learning-Based Asynchronous Sliding Mode Control for Switching Systems With Partly Unknown Probabilities

This study focuses on the learning-based asynchronous sliding mode control for switching systems, operating under a general switching rule and partially unknown probability information. A novel switching rule is constructed, governed by a joint probability distribution dependent on the current mode and its duration time, thereby overcoming the limitations of traditional Markov/semi-Markov models in terms of the difficulty in obtaining transition probabilities and computational complexity. Departing from traditional geometric distribution assumption, the proposed method follows more general duration distribution. Acknowledging the challenge of obtaining complete probability information in practical scenarios, partially unknown probability information is considered. In addition, a learning-based asynchronous sliding mode control law is developed, aimed at guiding state signals onto preset sliding regions and effectively reducing chattering induced by mode switchings. Finally, the efficacy and superiority of the developed theories are verified through both numerical and practical examples.