Stage‐cost design for optimal and model predictive control of linear port‐Hamiltonian systems: Energy efficiency and robustness

Abstract

AbstractWe consider singular optimal control of port‐Hamiltonian systems with minimal energy supply. We investigate the robustness of different stage‐cost designs w.r.t. time discretization and show that alternative formulations that are equivalent in continuous time, differ strongly in view of discretization. Furthermore, we consider the impact of additional quadratic control regularization and demonstrate that this leads to a considerable increase in energy consumption. Then, we extend our results to the tracking problem within model predictive control and show that the intrinsic but singular choice of the cost functional as the supplied energy leads to a substantial improvement of the closed‐loop performance.