Observer-based boundary control of distributed port-Hamiltonian systems

TL;DR

This paper introduces an observer-based boundary control method for infinite-dimensional port-Hamiltonian systems, utilizing finite-dimensional approximations to ensure stability and performance.

Contribution

It presents a constructive approach for designing boundary controllers and observers for infinite-dimensional systems using spatial discretization.

Findings

The method guarantees asymptotic stability of the interconnected system.

Performance improves as the finite-dimensional approximation approaches the infinite-dimensional model.

The approach is demonstrated on a Timoshenko beam model.

Abstract

An observer-based boundary controller for infinite-dimensional port-Hamiltonian systems defined on 1D spatial domains is proposed. The design is based on an early-lumping approach in which a finite-dimensional approximation of the infinite-dimensional system derived by spatial discretization is used to design the observer and the controller. As long as the finite-dimensional approximation approaches the infinite-dimensional model, the performances also do. The main contribution is a constructive method which guarantees that the interconnection between the controller and the infinite-dimensional system is asymptotically stable. A Timoshenko beam model has been used to illustrate the approach.