Port-Hamiltonian systems are becoming increasingly important in the modelling of physical systems. The key feature of this class of systems is the coupling of different subsystems using energy as the “lingua franca”. Although obtaining structure preserving space discretizations is quite straightforward, structured time discretizations of pH systems are more challenging. For the latter, the...
The lecture deals with numerical methods for solving port-Hamiltonian systems. The focus is on operator splitting methods. The aim is to derive high-order methods that preserve the port-Hamiltonian properties. Splitting methods with an order of three and higher have negative step sizes. As a result, the dissipation inequality is no longer preserved. Remedy create force-gradient methods. With...
Infinite-dimensional Hamiltonian systems offer an energy-based approach to model complex physical phenomena, appearing e.g. in fluid dynamics or mechanics. They are defined via a formally skew-symmetric Hamiltonian operator and are associated with a non-quadratic Hamiltonian energy function. In various applications, however, the Hamiltonian function depends on spatial derivatives of the state....
Regularization and index reduction for singular linear port-Hamilonian descriptor systems via output feedback is discussed. When the system is regularized and has index at most one, then the system is stable and passive, but not necessarily asymptotically stable and strictly passive. It is then shown how output feedback can be used to make the system (robustly) asymptotically stable and...
The framework of port-Hamiltonian (pH) systems allows to deduce structured models for physical systems from various domains. In recent work we have explored how the pH structure can be exploited in the analysis optimal control problems. Specifically, we consider the analysis of minimizing the energy supplied to the system while ensuring a set-point transition. We show that the pH structure...
Adaptive structures are ultra-lightweight structures with actuation distributed among the structural elements. They enable material savings in high-rise construction of about 50%. Energy-based methods offer advantages in modeling for coupling the mechanical structure with actuators from another domain, such as hydraulic, and also for the design of an energy-based controller or state estimator....
