Probabilistic Reach-Avoid Computation for Partially Degenerate Stochastic Processes

This work is concerned with the computation of probabilistic reach-avoid properties over a finite horizon for partially degenerate stochastic (that is, mixed deterministic-stochastic) processes evolving in discrete time over a continuous state-space. The models of interest consist of two fully coupled dynamical parts: the first part is described by deterministic maps (vector fields), whereas the second depends on probabilistic dynamics that are characterized by stochastic kernels. In contrast with a fully probabilistic approach (which is possible since the two dynamical components are coupled), this work shows that the probabilistic reach-avoid problem can be characterized-and thus computed-in two sequential steps: the first is a simple deterministic reachability analysis, which is then followed by a probabilistic reach-avoid problem depending on the outcome of the first step. This characterization leads to implementation advantages over a fully probabilistic approach and allows synthesizing a computational algorithm with explicit error bounds.