Optimization problems for structural acoustic models with thermoelasticity and smart materials

Lasiecka, Irena

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 20 (2000) no. 1, pp. 113-140.

Résumé

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.

Détail

Keywords: structural acoustic model with thermal effects, optimal control problem, smart controls, nonstandard Riccati equations, analyticity of semigroups

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