Distributed and backstepping boundary controls for port-Hamiltonian systems with symmetries

Abstract

International audienceA geometric spatial reduction for the port-Hamiltonian models is presented in this paper. It is based on the projection which makes use of the symmetries and on the preservation of the 'natural' power pairing for the considered system. Thanks to this reduction, an Interconnection and Damping Assignment Passivity Based Control (IDA-PBC-like) synthesis for infinite dimensional port-Hamiltonian systems is investigated. As for the finite dimensional case, a feedback control transforms the original model into a closed-loop target Hamiltonian model. Both distributed control and boundary control are used. The finite rank distributed control is determined to solve an average IDA-PBC matching equation. A backstepping boundary control is used to stabilize the matching error. The control model chosen to illustrate the approach is the so-called resistive diffusion equation for the radial diffusion of the poloidal magnetic flux

Twenty years of distributed port-Hamiltonian systems: a literature review

“…It is shown how a one-dimensional hyperbolic dpH system of two conservation laws can be shaped in a parabolic one. A similar idea was followed in Vu et al (2017a) where the IDA-PBC synthesis is explicitly addressed for a dpH system with spatial symmetries.…”