Casimir-Based Control Beyond the Dissipation Obstacle

TL;DR

This paper introduces a novel control approach for port-Hamiltonian systems that overcomes the dissipation obstacle by allowing controllers with negative semi-definite resistive structures, ensuring stability beyond traditional passive control methods.

Contribution

It demonstrates that stability can be achieved with controllers that have negative semi-definite resistive structures, surpassing the limitations of passive control.

Findings

Stability maintained with non-passive controllers.

Overcomes dissipation obstacle in port-Hamiltonian control.

Applicable to broader classes of systems.

Abstract

A prevailing trend in the stabilization of port-Hamiltonian systems is the assumption that the plant and the controller are both passive. In the standard approach of control by interconnection based on the generation of Casimir functions, this assumption leads to the dissipation obstacle, which essentially means that dissipation is admissible only on the coordinates of the closed-loop Hamiltonian that do not require shaping and thus severely restricts the scope of applications. In this contribution, we show that we can easily go beyond the dissipation obstacle by allowing the controller to have a negative semi-definite resistive structure, while guaranteeing stability of both the closed-loop and the controller.