Energy-optimal predictive control of discrete-time port-Hamiltonian systems: Closed-loop practical stability

Abstract

We study a dissipativity-based model predictive control (MPC) scheme for energy-optimal constrained output stabilization of a discrete-time nonlinear SISO port-Hamiltonian system described by difference and differential representation. For the optimal control problem to be solved in each MPC step, we establish a measure turnpike behavior. The turnpike set in our work is obtained from the underlying port-Hamiltonian structure without assuming existence of steady-states or periodic orbits. In particular, unlike existing results which typically establish the turnpike property w.r.t. a controlled forward invariant set such as optimal steady-states or optimal periodic orbits, we do not require the turnpike set to be forward control invariant. For MPC, we establish recursive feasibility and show practical stability to the turnpike set w.r.t. the MPC closed loop leveraging both dissipativity and the port-Hamiltonian structure. Finally, we demonstrate our results using two numerical examples.