Abstract
Abstract In this paper we present a dynamic programming based solution to a probabilistic reach-avoid problem for a controlled discrete time stochastic hybrid system. Similar to recent results related to the problem of probabilistic safety and stochastic target hitting, we introduce a sum-multiplicative cost function and a dynamic recursion that quantifies the probability of hitting a target set while avoiding an unsafe set. Optimal and worst-case reach while avoid control policies are introduced as the solution to an optimal control problem via dynamic programming. A computational example is provided.
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