# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1907.04705