Model Reduction on Manifolds: from a differential geometric formulation to data-driven realizations

Abstract: Port-Hamiltonian structures have a pervasive impact in numerous applied domains enlarging the more traditional mechanical one. While these structures are unequivocally characterized in the continuous-time domain, several descriptions are proposed in the literature when referring to discrete-time or sampled dynamics. In this talk we discuss a description of port-Hamiltonian structures in discrete time that makes reference to the notion of average passivity, introduced to deal with systems without throughput. Exploiting the average passivity property of these forms, we show how damping feedback and energy-based control strategies can be designed. Then, we investigate the sampled-data case and show how these forms set in discrete-time can be recovered under time-integration through modification of the interconnection and dissipation matrices characterizing the continuous-time dynamics. Some simulations are presented to illustrate analysis and control performances.

mathematical physicsanalysis of PDEsdifferential geometrydynamical systemsfunctional analysisnumerical analysisoptimization and controlspectral theory

Audience: researchers in the discipline

( slides )

Port-Hamiltonian Seminar

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