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Mean Square Optimal Control by Interconnection for Linear Stochastic Hamiltonian Systems

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Document pages: 9 pages

Abstract: This paper is concerned with linear stochastic Hamiltonian (LSH) systemssubject to random external forces. Their dynamics are modelled by linearstochastic differential equations, parameterised by stiffness, mass, dampingand coupling matrices. A class of physical couplings is discussed for suchsystems using inerters, springs and dampers. We consider a problem ofminimising a steady-state quadratic cost functional over the couplingparameters for the interconnection of two LSH systems, one of which plays therole of an analog controller. For this mean square optimalcontrol-by-interconnection setting, we outline first-order necessary conditionsof optimality which employ variational methods developed previously forconstrained linear quadratic Gaussian control problems.

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