Ricardo Sanfelice - University of California, Santa Cruz Hybrid systems model the behavior of dynamical systems in which the states can evolve continuously and, at isolate time instances, exhibit instantaneous jumps. Such systems arise when control algorithms need to rapidly react due to changes in the physics or in the environment. In vehicle applications, the typically abrupt emergence of a pedestrian or of another vehicle typically lead to rapid reactions by the algorithms onboard the vehicle, in particular, to assure safety. In this talk, we present a set-based predictive control framework for control and prediction with hybrid dynamics. To account for uncertainties, the set-based controller generalizes conventional model predictive control and predicts the set that the state of a dynamical system might belong to. This generalization is used to formulate collision avoidance as a hard constraint in a (set-based and hybrid) predictive control algorithm. The framework and ideas are illustrated in a vehicle application with dynamic obstacles and optimized trajectories with the goal of safely guiding a vehicle towards a target.