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We study the finite-horizon optimal control problem with quadraticfunctionals for an established fluid-structure interaction model. The coupledPDE system under investigation comprises a parabolic (the fluid) and ahyperbolic (the solid) dynamics; the coupling occurs at the interface betweenthe regions occupied by the fluid and the solid. We establish several traceregularity results for the fluid component of the system, which are thenapplied to show well-posedness of the Differential Riccati Equations arising inthe optimization problem. This yields the feedback synthesis of the uniqueoptimal control, under a very weak constraint on the observation operator; inparticular, the present analysis allows general functionals, such as theintegral of the natural energy of the physical system. Furthermore, this workconfirms that the theory developed in Acquistapace et al. [Adv. DifferentialEquations, 2005] -- crucially utilized here -- encompasses widely differing PDEproblems, from thermoelastic systems to models of acoustic-structure and, now,fluid-structure interactions.

Optimal boundary control with critical penalization for a PDE model of fluid-solid interactions