On second order conditions for singular optimal control of port-Hamiltonian systems

TL;DR

This paper investigates second order optimality conditions for singular control problems in port-Hamiltonian systems, providing new theoretical insights and extending results to nonlinear descriptor systems.

Contribution

It derives novel second order optimality conditions for singular controls in port-Hamiltonian systems, including both ordinary and descriptor cases, with a focus on energy-based cost functionals.

Findings

Derived optimality conditions for control-affine port-Hamiltonian systems.

Extended results to nonlinear port-Hamiltonian descriptor systems.

Provided elegant conditions especially in the linear case.

Abstract

We study nonlinear singular optimal control problems of port-Hamil-tonian (descriptor) systems. We employ general control-affine cost functionals that include as a special case the energy supplied to the system. We first derive optimality conditions for the case of ordinary differential equations with and without control bounds by applying the general theory to the specially structured port-Hamiltonian case, and show that this leads to elegant optimality conditions, in particular in the linear case. We then extend these results to classes of nonlinear port-Hamiltonian descriptor systems.