Probabilistic Reachability and Invariance Computation of Stochastic Systems using Linear Programming

TL;DR

This paper presents methods to evaluate the safety of discrete-time stochastic systems over finite horizons by linking probabilistic invariance with reachability and reach-avoid problems, using dynamic and linear programming techniques.

Contribution

It introduces an efficient approach to compute probabilistic invariance and reachability for stochastic systems through linear programming.

Findings

Efficient computation of probabilistic invariance and reachability.

Linking invariance with reach-avoid problems.

Application of linear programming to stochastic safety analysis.

Abstract

We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute these quantities using dynamic and linear programming.