Safety-Probability Analysis and Control for Stochastic Systems Based on Lyapunov Candidate Functions

In recent control theory, safety analysis and safety-critical control based on a (control) barrier function have been actively pursued. The barrier function is closely related to a Lyapunov function, which is an important property that guarantees asymptotic stability of the system, i.e., the settling to the target state, which is a fundamental control performance. Therefore, control strategies that simultaneously guarantee safety and stability are important in the recent control scene. In this paper, we propose a method for quantitative evaluation of safety probability for stochastic systems based on barrier functions generated from Lyapunov functions, and then develop control design methods to increase the safety probability. In particular, safety analysis and safety-critical control of linear stochastic systems having additive noises are performed based on linear algebra. We also discuss design methods for safety and safety-critical control for input-affine stochastic systems. The effectiveness of the proposed method is demonstrated based on a simple example.