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. Note to Practitioners—With the rapid development of networked control technologies, designing switching rules for switching systems and suppressing chattering in sliding mode control remain key challenge. In practical engineering systems, such as power systems, robotic control, and networked systems, the duration of different modes is often influenced by external disturbances, equipment characteristics, and load variations, making it difficult to model simply as a geometric distribution. Meanwhile, traditional Markov/semi-Markov models rely on extensive statistical data, and their transition probabilities are challenging to obtain accurately in practice. To address these issues, a joint probability distribution function based on the current mode and its duration, is adopted to accurately reflect the duration characteristics of the system in different states while reducing computational burden. The duration distribution, which depends on the current mode, is characterized by a general distribution, making the model more applicable to complex engineering systems. Furthermore, in industrial applications, sliding mode control often suffers from chattering issues caused by system modes, asynchronous double switching, discontinuities in the sign function, and other factors. As considered in this paper, a novel learning-based asynchronous sliding mode control method, incorporating emission probability and iterative learning, is proposed to alleviate chattering in sliding mode control.