Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian Learning

Despite the existence of numerous designs, significant research efforts, and successful applications in the field of control systems, the development of a reliable and secure controller that combines robust theoretical foundations with exceptional performance continues to present a formidable challenge. This challenge has captured the attention of researchers from diverse fields, including robotics [1] and healthcare [2], among others. In the context of control systems, safety is evaluated based on the system state. In this study, we focus on probabilistic safe control, wherein a safe controller is expected to prevent the system from entering hazardous states with an acceptable probability [3-5]. Due to the intricate nature of calculating the safe state space for a general dynamics-driven system, ensuring safety by designing or learning a safe controller is rather complex. Existing safe control strategies include model predictive control [6], reachability analysis [7], and control barrier function (CBF) method [8]. In our research, we build upon the CBF method, which ensures that the system state remains within safe regions by defining a forward invariant set. This set is a subset of the safe region and restricts the system state within its boundaries. Furthermore, we take into account the presence of uncertainty, which not only have a more significant impact on the system state than small disturbances [9], and does not have an analytical format as well [10].