Abstract
A class of steady-state stochastic regulator problems for abstract wave equations in a Hilbert space—of relevance to the problem of feedback control of large space structures using co-located controls/sensors—is studied. Both the control operator, as well as the observation operator, are finite-dimensional. As a result, the usual condition of exponential stabilizability invoked for existence of solutions to the steady-state Riccati equations is not valid. Fortunately, for the problems considered it turns out that strong stabilizability suffices. In particular, a closed form expression is obtained for the minimal (asymptotic) performance criterion as the control effort is allowed to grow without bound.
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