Model Predictive Control of Coupled Hyperbolic PDEs and ODEs

The paper addresses model predictive control design for a set of coupled hyperbolic PDEs and ODEs. The PDEs and ODEs system are connected through the boundary of PDEs system. The overall system contains infinite-dimensional state space extended with the finite-dimensional state space which provides the framework for constrained optimal control law realization. In this work, the discrete PDEs-ODEs system is obtained by using Cayley-Tustin time discretization without applying spatial approximation of underlying PDEs. The model predictive control is designed by utilizing standard constrained optimization obtained control law which leads to quadratic regulator design accounting for input or/and state/output constraints. Finally, the controller performance is assessed by a numerical simulation.