On Structural Invariants in the Energy-Based Control of Infinite-Dimensional Port-Hamiltonian Systems with In-Domain Actuation

TL;DR

This paper develops an energy-based control method for infinite-dimensional port-Hamiltonian systems with in-domain actuation, utilizing a jet-bundle formalism and structural invariants to achieve control of PDE-governed systems like beams and plates.

Contribution

It introduces a novel control approach based on structural invariants for PDE systems described by port-Hamiltonian formalism with in-domain actuation.

Findings

Effective control of beam and plate systems demonstrated.

Structural invariants enable stable energy-based control.

Applicable to systems with second-order Hamiltonian.

Abstract

This contribution deals with energy-based in-domain control of systems governed by partial differential equations with spatial domain up to dimension two. We exploit a port-Hamiltonian system description based on an underlying jet-bundle formalism, where we restrict ourselves to systems with 2nd-order Hamiltonian. A certain power-conserving interconnection enables the application of a dynamic control law based on structural invariants. Furthermore, we use various examples such as beams and plates with in-domain actuation to demonstrate the capability of our approach.