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We present a model predictive control (MPC) algorithm for the appropriate discretizations of (nondiscretized) hybrid dynamical systems. The optimization problem associated with the MPC algorithm is formulated with a set-based prediction horizon and the discretized hybrid dynamics as part of its constraints. Sufficient conditions guaranteeing structural properties of the problem and asymptotic stability of a closed set are revealed. These conditions include the existence of a control Lyapunov function assuring an invariance property on the terminal constraint set. In addition, we formulate a method to obtain numerical solutions to the hybrid optimal control problem, amenable to off-the-shelf optimization solvers, and demonstrate this method on the discretization of a prototypical hybrid system.

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