Average-price and reachability-price games on hybrid automata with strong resets

We introduce and study hybrid automata with strong resets. They generalize o-minimal hybrid automata, a class of hybrid automata which allows modeling of complex continuous dynamics. A number of analysis problems, such as reachability testing and controller synthesis, are decidable for classes of o-minimal hybrid automata. We generalize existing decidability results for controller synthesis on hybrid automata and we establish new ones by proving that average-price and reachability-price games on hybrid systems with strong resets are decidable, provided that the structure on which the hybrid automaton is defined has a decidable first-order theory. Our proof techniques include a novel characterization of values in games on hybrid systems by optimality equations, and a definition of a new finitary equivalence relation on the states of a hybrid system which enables a reduction of games on hybrid systems to games on finite graphs