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Discrete Time Stochastic Hybrid Dynamic Games : Part I-Formulation & Applications

We formulate a framework for discrete time stochastic hybrid dynamic game with two players and consider the reach-avoid problem, i.e. finding the probability that the system trajectory starting from any initial condition enters a target set while avoiding the obstacle set in a given time-horizon. We formulate the reach-avoid problem as a zero-sum stochastic game and show that the verification and controller synthesis of the reach-avoid game can be addressed using an appropriate dynamic programming algorithm. The utility of this modeling and analysis framework is shown with two applications: a stochastic pursuit-evasion game between two aircraft, and a quadtrotor tracking a ground vehicle.