Model Predictive Control for Hybrid Dynamical Systems: Sufficient Conditions for Asymptotic Stability with Persistent Flows or Jumps

Recent results on asymptotically stabilizing model predictive control for hybrid dynamical systems are relaxed by exploiting basic knowledge about the structure of the set of trajectories. Specifically, it is shown that when the system to be controlled has trajectories with infinitely many discrete transitions, the cost functional of the underlying optimal control problem does not need to weight the state and the input in continuous time. An analogue of this result shows that when trajectories are defined over all ordinary time, the functional does not need to weight the state and the input during discrete transitions. Results are demonstrated with recurring examples.