Geometric Scattering in Tele-manipulation of Port Controlled Hamiltonian Systems

In this paper we study the interconnection of two port controlled Hamiltonian systems through a transmission line with delay. The contributions of the paper are firstly a geometrical, multi-dimensional, power consistent exposition of tele-manipulation of Intrinsically Passive Controlled (IPC) physical systems, with a clarification on impedance matching, and secondly a system theoretic condition for the adaptation of a general port controlled Hamiltonian system with dissipation (PCHD system) to a transmission line. To the knowledge of the authors, the latter result in particular has never appeared in such a general form. Experimental results on an Internet implementation are also presented.