Abstract
We present a model predictive control (MPC) algorithm for hybrid dynamical systems. The proposed algorithm relies on a terminal constraint and a cost function, as well as a set-based notion of prediction horizon, reminiscent of free end-time optimal control problems. When the terminal cost is a control Lyapunov function (CLF) on the terminal constraint set, and the prediction horizon has a certain geometry, under standard assumptions from conventional MPC, the closed-loop system governed by MPC is shown to have an asymptotically stable compact set using the value function. A numerical example using the prototypical hybrid model of a bouncing ball demonstrates the effectiveness of the proposed algorithm.
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