Discrete Port-Hamiltonian Systems

Authors:	Talasila Viswanath, Imperial College, London, United Kingdom Clemente-Gallardo Jesus, Instituto de Biocomputacion y Fisica de los Sistemas Complejos, Spain van der Schaft Arjan, Universiteit Twente, Netherlands
Topic:	2.3 Non-Linear Control Systems
Session:	Geometric Network Modeling and Control of Complex Physical Systems
Keywords:	Port Hamiltonian systems, discrete mechanics.

Abstract

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling at the discrete level itself. One of the goals of this paper is to model Port-Hamiltonian systems at the discrete level. We also show that the dynamics of the discrete models we obtain exactly correspond to the dynamics obtained via a usual discretization procedure. In this sense we offer an alternative to the usual procedure of modeling (at the smooth level) and discretization.