A Differential Riccati Equation for the Active Control of a Problem in Structural Acoustics
نویسنده
چکیده
In this paper, we provide results concerning the optimal feedback control of a system of partial di erential equations which arises within the context of modelling a particular uid/structure interaction system seen in structural acoustics, this application being the primary motivation for our work. This model onsists of two coupled PDE's exhibiting parabolic and hyperbolic characteristics respectively; the control action, in this case, is modelled by a highly unbounded operator. We rigorously justify a optimal control theory or this class of problems and characterize the optimal control through a suitable Riccati Equation. This is achieved, in part, by exploiting recent techniques in the area of optimization of analytic systems with unbounded inputs, along with a local microanalysis of the hyperbolic part of the dynamics, an analysis which will consider the propagation of singularities and optimal \trace" behavior of the solutions.
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