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Reachability of Diffusions via Optimal Control


P. Mohajerin Esfahani

IfA Internal Seminar Series

We develop a novel framework for formulating a class of stochastic reachability problems with state constraints as a stochastic optimal control problem. Previous approaches to solving these problems are either confined to the deterministic setting or address almost-sure stochastic notions. In contrast, we propose a new methodology to tackle probabilistic specifications that are less specific than almost sure requirements. To this end, we first establish a connection between two stochastic reach-avoid problems and classes of different stochastic optimal control problems for diffusions with discontinuous payoff functions. In the sequel, we shall focus on one of the class of stochastic optimal control problem, exit-time problem, which indeed addresses both reachability type questions. We derive a weak version of dynamic programming principle (DPP) for the value functions. Moreover, based on our DPP, we give an alternate characterization of the value function as the solution to a partial differential equation in the sense of discontinuous viscosity solutions. Finally we validate the performance of the proposed framework on the stochastic Zermelo navigation problem.


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