Energy-optimal control of infinite-dimensional Port-Hamiltonian systems with an application to adaptive buildings

• Applicants: Dr. Friedrich Maximilian Philipp; Professor Dr. Manuel Schaller
• Subject Area: Mathematics ; Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 554600805

The energy-based Hamiltonian formulation of physical processes already replaced the Newtonian kinetic formulation at the beginning of the nineteenth century. In the nineties, these system models were extended by modular structures - the so-called ports. Such port-Hamiltonian systems can be used to model not only mechanical processes, but also those from many other areas of physics. This research project addresses the optimal control problem that aims at transforming the state of an infinite-dimensional port-Hamiltonian system into another one with minimal energy supply and output tracking subject to control constraints. In this context, the considered cost functional is application-driven from both a physical and an engineering point of view and is strongly intertwined with the port-Hamiltonian dynamics. Since it depends linearly on the control, the optimization task falls into the class of singular optimal control problems, which are generally difficult to treat both analytically and numerically. However, in the present case, the port-Hamiltonian structure and the existing intrinsic relation between the objective function and the dynamics can be used to resolve the singularity and prove manifold properties of optimal solutions. The goal of the project is, on the one hand, the rigorous structure-exploiting proof of hidden regularities in the optimality system, by which an optimal state feedback can be given analogous to the classical linear-quadratic regulator. On the other hand, it will be shown that optimal trajectories of the above singular problem exhibit a stable long-time behavior - the so-called turnpike property. This means that optimal states or controls are stationary in a certain sense in the long run. Knowledge of such behavior can be exploited numerically in a variety of ways and is an important part in the analysis of model predictive controllers. The results obtained will be used to design energy-optimal controllers in adaptive building control. In this application, controllable beams are used to save - especially in the construction of high-rise buildings - CO2-intensive concrete, which is usually installed to ensure stiffness.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr. Karl Worthmann