Energy-based Control and Observer Design for higher-order infinite-dimensional Port-Hamiltonian Systems

TL;DR

This paper introduces an energy-based control and observer design method for infinite-dimensional port-Hamiltonian systems, demonstrated on a Kirchhoff-Love plate, enabling effective control despite unmeasurable states.

Contribution

It develops a novel control and observer design framework for boundary-actuated port-Hamiltonian systems with second-order Hamiltonian, extending energy-Casimir methods to infinite dimensions.

Findings

Successful control of a Kirchhoff-Love plate example

Design of an observer for unmeasurable states

Extension of energy-Casimir method to infinite-dimensional systems

Abstract

In this paper, we present a control-design method based on the energy-Casimir method for infinite-dimensional, boundary-actuated port-Hamiltonian systems with two-dimensional spatial domain and second-order Hamiltonian. The resulting control law depends on distributed system states that cannot be measured, and therefore, we additionally design an infinite-dimensional observer by exploiting the port-Hamiltonian system representation. A Kirchhoff-Love plate serves as an example in order to demonstrate the proposed approaches.