Discretization of port-Hamiltonian systems

Abstract: Controller design for distributed parameter systems is often accomplished using a lumped approximation. For a system that is exponentially stable, it is reasonable to expect the approximation to preserve this decay rate. Preservation of the decay rate is important for realistic simulations and also for reliable controller design. An example illustrating the problems that can occur even in a simple problem will be given. It will be shown that a number of standard methods - not all - are structure-preserving for a class of port-Hamiltonian systems. Most importantly, when these systems are exponentially stable, a uniform decay rate is preserved by the approximations. The method is to show that a modification of the energy yields a Lyapunov function. The results are illustrated with simulations of an example of LQ-optimal controller design.

mathematical physicsanalysis of PDEsdifferential geometrydynamical systemsfunctional analysisnumerical analysisoptimization and controlspectral theory

Audience: researchers in the discipline

Port-Hamiltonian Seminar

Series comments: Slides and recordings can be found here: uni-wuppertal.sciebo.de/s/CQfBsXr9iOI17ZY