Model Predictive Control of Impulsive Dynamical Systems

We propose an MPC framework to address impulsive dynamical systems, i.e. systems in which the state trajectories are permitted to have discontinuities (jumps) in response to impulsive controls. We describe how previous results on sampled-data trajectories, invariance of sets, optimal control, and stability in the context of impulsive systems can be used and adapted to a sampled-data MPC framework. We provide sufficient conditions on the design parameters of the optimal control problems that guarantee: (i) feasibility of the sequence of optimal control problems, and (ii) stability of the controlled system.