Ding, JerryKamgarpour, MaryamSummers, SeanAbate, AlessandroLygeros, JohnTomlin, Claire2021-12-012021-12-012021-12-012013-0910.1016/j.automatica.2013.05.025https://infoscience.epfl.ch/handle/20.500.14299/183380We describe a framework for analyzing probabilistic reachability and safety problems for discrete time stochastic hybrid systems within a dynamic games setting. In particular, we consider finite horizon zero-sum stochastic games in which a control has the objective of reaching a target set while avoiding an unsafe set in the hybrid state space, and a rational adversary has the opposing objective. We derive an algorithm for computing the maximal probability of achieving the control objective, subject to the worst-case adversary behavior. From this algorithm, sufficient conditions of optimality are also derived for the synthesis of optimal control policies and worst-case disturbance strategies. These results are then specialized to the safety problem, in which the control objective is to remain within a safe set. We illustrate our modeling framework and computational approach using both a tutorial example with jump Markov dynamics and a practical application in the domain of air traffic management.text::journal::journal article::research article