A Class of Discrete-Time Port-Hamiltonian Systems. Modelling and Control Design

Abstract: In this talk, we present a general approach to derive discrete-time approximations of lumped and distributed-parameter port-Hamiltonian systems. Since the goal is to preserve passivity, the key ingredient has been to replace the gradient of the Hamiltonian function that appears in the continuous-time dynamics with a discrete gradient. In this way, the discrete-time approximation inherits the passivity of the initial continuous-time dynamics. In finite dimensions, the result is a state equation in implicit form, while for linear boundary control systems, we obtain a boundary-value problem to be solved at each step. In both cases, the well-posedness of the resulting discrete-time dynamics is discussed. Regarding control design, the continuous-time energy-shaping plus damping injection technique is extended to the discrete-time scenario. In the final part of the talk, we briefly discuss the problem of coupling the digital controller with the continuous-time plant and the use of such models in a model predictive control scheme.

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