Mean Square Optimal Control by Interconnection for Linear Stochastic Hamiltonian Systems

TL;DR

This paper develops a method for optimally controlling linear stochastic Hamiltonian systems by interconnecting two such systems, minimizing a quadratic cost through variational techniques, with applications involving physical couplings like inerters, springs, and dampers.

Contribution

It introduces a mean square optimal control framework for interconnected stochastic Hamiltonian systems, extending variational methods to this class of problems.

Findings

Derivation of first-order necessary conditions for optimality.

Application of variational methods to control of stochastic Hamiltonian systems.

Framework accommodates physical couplings such as inerters, springs, and dampers.

Abstract

This paper is concerned with linear stochastic Hamiltonian (LSH) systems subject to random external forces. Their dynamics are modelled by linear stochastic differential equations, parameterised by stiffness, mass, damping and coupling matrices. A class of physical couplings is discussed for such systems using inerters, springs and dampers. We consider a problem of minimising a steady-state quadratic cost functional over the coupling parameters for the interconnection of two LSH systems, one of which plays the role of an analog controller. For this mean square optimal control-by-interconnection setting, we outline first-order necessary conditions of optimality which employ variational methods developed previously for constrained linear quadratic Gaussian control problems.