Regeneratively-constrained LQG control of passive networks ?

In this paper we consider the synthesis of optimal feedback controllers for a stochastically-excited passive electromechanical network, subject to the constraint that in stationarity, the feedback law must be realizable with a regenerative actuation system. Regenerative systems are similar to passive systems but their dynamic constraints are more relaxed, in the sense that they only need to conserve energy in the stationary average sense, rather than at every time instant. In this paper, we examine the design of optimal LQG controllers for passive networks controlled with regenerative actuation. We show that this problem may be posed as a multi-objective LMI problem. We also characterize how close a regeneratively-constrained optimal LQG feedback law is to a passive transfer function. The concepts are demonstrated on a simple example related to vibration suppression.