Alternative passive maps in the Brayton-Moser framework: Implications on control and optimization

TL;DR

This paper explores alternative passive maps within the Brayton-Moser framework, addressing control and optimization challenges in passivity-based control, especially overcoming the dissipation obstacle in finite-dimensional systems.

Contribution

It introduces new passive maps in the Brayton-Moser framework that facilitate control design and optimization, overcoming existing limitations like the dissipation obstacle.

Findings

New passive maps enable control of systems with bounded power and unbounded energy.

The Brayton-Moser framework is extended to improve control design flexibility.

Addressing PDEs and storage functions enhances the applicability of passivity-based control.

Abstract

In the recent years, passivity theory has gained renewed attention because of its advantages and practicality in modeling of multi-domain systems and constructive control techniques. Unlike Lyapunov theory, passivity theory takes a behavioral approach in its control design methodologies. Hence, it provides solutions, which not only achieve the control objectives, but are also easily interpretable in the standard engineering parlance. The fundamental idea in passivity based control (PBC) methodologies is to find a controller that renders the closed-loop system passive. It is well known that, the PBC methodologies that rely on power-conjugate port-variables do not work for control objectives that require bounded power and unbounded energy. This is commonly known as the dissipation obstacle. One possible alternative that has been well explored, in the case of finite dimensional systems, is Brayton-Moser formulation. However, designing controllers in this framework leads to various difficulties, such as, solving for partial differential equations and finding storage functions satisfying a gradient structure.