Lasiecka, Irena Optimization problems for structural acoustic models with thermoelasticity and smart materials. (English) Zbl 0964.35021 Discuss. Math., Differ. Incl. Control Optim. 20, No. 1, 113-140 (2000). Summary: An optimization problem for a structural acoustic model with controls governed by unbounded operators on the state space is considered. This type of controls arises naturally in the context of “smart material technology”. The main result of the paper provides an optimal synthesis and solvability of associated nonstandard Riccati equations. It is shown that in spite of the unboundedness of control operators, the resulting gain operators (feedbacks) are bounded on the state space. This allows to provide full solvability of the associated Riccati equations. The proof of the main result is based on exploiting propagation of analyticity from the structural component of the model into an acoustic medium. Cited in 4 Documents MSC: 35B37 PDE in connection with control problems (MSC2000) 35L70 Second-order nonlinear hyperbolic equations 93D15 Stabilization of systems by feedback 35B40 Asymptotic behavior of solutions to PDEs 47D06 One-parameter semigroups and linear evolution equations Keywords:structural acoustic model with thermal effects; smart controls; nonstandard Riccati equations; analyticity of semigroups PDFBibTeX XMLCite \textit{I. Lasiecka}, Discuss. Math., Differ. Incl. Control Optim. 20, No. 1, 113--140 (2000; Zbl 0964.35021) Full Text: DOI