Structure-preserving discretization for port-Hamiltonian descriptor systems
For researchers in modeling and simulation of physical systems, this work provides a theoretical extension and structure-preserving discretization results, but the numerical examples are limited and no concrete performance gains are reported.
The paper extends port-Hamiltonian descriptor systems to under- and over-determined cases with arbitrary differentiable Hamiltonians, and shows that certain time-discretization methods preserve the structure under assumptions on the Hamiltonian.
We extend the modeling framework of port-Hamiltonian descriptor systems to include under- and over-determined systems and arbitrary differentiable Hamiltonian functions. This structure is associated with a Dirac structure that encloses its energy balance properties. In particular, port-Hamiltonian systems are naturally passive and Lyapunov stable, because the Hamiltonian defines a Lyapunov function. The explicit representation of input and dissipation in the structure make these systems particularly suitable for output feedback control. It is shown that this structure is invariant under a wide class of nonlinear transformations, and that it can be naturally modularized, making it adequate for automated modeling. We investigate then the application of time-discretization schemes to these systems and we show that, under certain assumptions on the Hamiltonian, structure preservation is achieved for some methods. Numerical examples are provided.