Concetti Chiave
This paper proposes novel barrier-like sufficient conditions to compute both lower and upper bounds of the probability that a stochastic discrete-time system will exit a safe set or reach a target set within a given bounded time horizon.
Sintesi
The paper studies finite-time safety and reach-avoid verification for stochastic discrete-time dynamical systems. The goal is to determine lower and upper bounds of the probability that, within a predefined finite-time horizon, a system starting from an initial state in a safe set will either exit the safe set (safety verification) or reach a target set while remaining within the safe set until the first encounter with the target (reach-avoid verification).
The key highlights are:
- The paper introduces novel barrier-like sufficient conditions for characterizing these probability bounds, which either complement existing ones or fill gaps.
- For finite-time safety verification, the proposed conditions in Theorem 1 and 2 provide both lower and upper bounds, going beyond existing works that only offered upper bounds.
- For finite-time reach-avoid verification, the conditions in Theorem 3 and 5 also compute both lower and upper bounds of the probability.
- The proposed conditions are more expressive than previous barrier function-based methods, allowing for a wider range of parameters.
- The effectiveness of the proposed conditions is demonstrated on two numerical examples using semi-definite programming.