Control Barrier Functions for Stochastic Systems With Quantitative Evaluation of Probability

Yuki Nishimura, Kenta Hoshino

In recent years, the analysis of a control barrier function has received considerable attention because it is helpful for the safety-critical control required in many control application problems. However, the extension of the analysis to a stochastic system remains a challenging issue. In this paper, we consider sufficient conditions for almost-sure-type reciprocal and zeroing control barrier functions and design a control law. Then, we propose another version of a stochastic zeroing control barrier function to evaluate a probability of a sample path staying in a safe set and confirm the convergence of a specific expectation related to the attractiveness of a safe set. We also discuss the robustness of safety against changing a diffusion coefficient. Finally, we confirm the validity of the proposed control design and the analysis using the control barrier functions via simple examples with their numerical simulation.

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