Distributed and backstepping boundary controls to achieve IDA-PBC design

Abstract

An IDA-PBC-like control 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.