Maximum Power Transfer for Nonlinear State Space Systems

TL;DR

This paper extends the classical maximum power transfer theorem to nonlinear state space systems using a Hamiltonian framework, providing a new method to determine optimal loads in complex physical systems.

Contribution

It introduces a nonlinear generalization of the maximum power transfer theorem using Hamiltonian input-output systems and Pontryagin's Maximum principle.

Findings

Derived a state space version of the maximum power transfer theorem.

Formulated a Hamiltonian input-output system related to Pontryagin's principle.

Analyzed the structure of optimal loads for various physical systems.

Abstract

The classical Maximum Power Transfer theorem of linear electrical network theory is generalized to the setting of a nonlinear state space system connected to a source. This yields a state space version of the input-output operator results of Wyatt (1988). Key tool in the analysis is the formulation of a Hamiltonian input-output system, which is closely related to Pontryagin's Maximum principle. The adjoint variational system incorporated in this system defines an optimal load. The structure of such an optimal load is investigated for classes of physical systems.