Energy-Based Control of Nonlinear Infinite-Dimensional Port-Hamiltonian Systems with Dissipation

TL;DR

This paper develops energy-based control methods for nonlinear infinite-dimensional port-Hamiltonian systems with dissipation, focusing on PDEs with 1D spatial domain and second-order Hamiltonians, demonstrated on a nonlinear Euler-Bernoulli beam.

Contribution

It introduces a novel control framework for nonlinear PDE port-Hamiltonian systems with dissipation, utilizing Casimir functionals and energy balancing techniques.

Findings

Effective energy-based control for nonlinear PDE systems demonstrated on Euler-Bernoulli beam.

Incorporation of dissipation models within the port-Hamiltonian framework.

Analysis of control strategies using Casimir functionals.

Abstract

In this paper, we consider nonlinear PDEs in a port-Hamiltonian setting based on an underlying jet-bundle structure. We restrict ourselves to systems with 1-dimensional spatial domain and 2nd-order Hamiltonian including certain dissipation models that can be incorporated in the port- Hamiltonian framework by means of appropriate differential operators. For this system class, energy-based control by means of Casimir functionals as well as energy balancing is analysed and demonstrated using a nonlinear Euler-Bernoulli beam.