Refined Barrier Conditions for Finite-Time Safety and Reach-Avoid Guarantees in Stochastic Systems
For safety-critical stochastic systems, this work expands the class of verifiable systems by relaxing a key assumption, enabling broader applicability of barrier methods.
This paper removes a restrictive boundedness assumption in barrier methods for stochastic systems, enabling finite-time safety and reach-avoid guarantees for systems with unbounded state spaces. The approach is demonstrated via numerical examples.
Providing finite-time probabilistic safety and reach-avoid guarantees is crucial for safety-critical stochastic systems. Existing state-of-the-art barrier methods often rely on a restrictive boundedness assumption for auxiliary functions, limiting their applicability. This paper presents refined barrier conditions that remove this assumption. Specifically, we establish conditions for deriving upper bounds on finite-time safety probabilities in discrete-time systems and lower bounds on finite-time reach-avoid probabilities in continuous-time systems. This relaxation expands the class of verifiable systems, especially those with unbounded state spaces, and facilitates the use of advanced optimization techniques, such as semi-definite programming with polynomial functions. Numerical examples demonstrate the effectiveness of the approach.