A Simple Model-Predictive Control Strategy for Discrete-Time Port-Hamiltonian Boundary Control Systems

This paper deals with discrete-time linear boundary control systems (BCSs) in port-Hamiltonian form, for which the discretization is performed in time while preserving the distributed nature of the state and the passivity of the original system. The contribution is twofold. First, an explicit parametrized expression of the discrete-time state evolution is derived. Second, this parametrization is employed to design a simple model predictive control (MPC) law. The receding-horizon scheme relies on an optimization procedure based on a quadratically constrained quadratic programming (QCQP) problem. By following standard arguments and exploiting the passivity of the BCS, we prove that the MPC methodology guarantees asymptotic stability.