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In this paper, we address the stochastic reach-avoid problem for linearsystems with additive stochastic uncertainty. We seek to compute the maximumprobability that the states remain in a safe set over a finite time horizon andreach a target set at the final time. We employ sampling-based methods andprovide a lower bound on the number of scenarios required to guarantee that ourestimate provides an underapproximation. Due to the probabilistic nature of thesampling-based methods, our underapproximation guarantee is probabilistic, andthe proposed lower bound can be used to satisfy a prescribed probabilisticconfidence level. To decrease the computational complexity, we propose aVoronoi partition-based to check the reach-avoid constraints at representativepartitions (cells), instead of the original scenarios. The state constraintsarising from the safe and target sets are tightened appropriately so that thesolution provides an underapproximation for the original sampling-based method.We propose a systematic approach for selecting these representative cells andprovide the flexibility to trade-off the number of cells needed for accuracywith the computational cost.

Voronoi Partition-based Scenario Reduction for Fast Sampling-based Stochastic Reachability Computation of LTI Systems