Safety-Critical Control of Stochastic Systems using Stochastic Control Barrier Functions

TL;DR

This paper introduces stochastic control barrier functions (SCBFs) for safety-critical control of stochastic systems, reducing control effort and providing less conservative safety estimates compared to existing methods, with theoretical and simulation validation.

Contribution

The paper proposes a new class of stochastic control barrier functions (SCBFs) that improve safety and efficiency in stochastic systems, extending to high-order constraints.

Findings

SCBFs reduce control efforts in noisy environments.

SCBFs offer less conservative safety probability estimates.

Numerical simulations validate theoretical results.

Abstract

Control barrier functions have been widely used for synthesizing safety-critical controls, often via solving quadratic programs. However, the existence of Gaussian-type noise may lead to unsafe actions and result in severe consequences. In this paper, we study systems modeled by stochastic differential equations (SDEs) driven by Brownian motions. We propose a notion of stochastic control barrier functions (SCBFs)and show that SCBFs can significantly reduce the control efforts, especially in the presence of noise, compared to stochastic reciprocal control barrier functions (SRCBFs), and offer a less conservative estimation of safety probability, compared to stochastic zeroing control barrier functions (SZCBFs). Based on this less conservative probabilistic estimation for the proposed notion of SCBFs, we further extend the results to handle high relative degree safety constraints using high-order SCBFs. We demonstrate that the proposed SCBFs achieve good trade-offs of performance and control efforts, both through theoretical analysis and numerical simulations.