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Wellposedness of optimal control problems for systems with unbounded controls and partially analytic generators

Lasiecka I.

Control and Cybernetics

2002

Vol. 31, no 3

751-777

Wellposedness of differential and algebraic Riccati equations for control systems with unbounded control operators is considered. It is shown that the full-classical Riccati theory is recovered for a class of dynamics, whose generators are partially analytic. Partial analyticity is quantitatively expressed by the validity of the so-called "singular estimates", which is imposed on the composition operator E[sup At]B (A is the generator, B is unbounded control operator. This class comprises the PDE coupled systems with hyperbolic and parabolic components. Two illustrative examples are given in the paper: boumdary/point control of thermal plates with hyperbolic character and point control of structural acoustic interactions. The latter are described by wave equation coupled at an interface to a plate equation.

Uniform stability in structural acoustic systems with thermal effects and nonlinear boundary damping

Lasiecka I., Lebiedzik C.

Control and Cybernetics

1999

Vol. 28, no 3

557-581

The stabilization problem for a structural acoustic model is considered. The model under consideration is that of acoustic cavity (wave equation) coupled at the interface with a flexible wall (plate equation) which accounts for thermal effects. It is shown that frictional, nonlinear damping applied at the boundary of the acoustic chamber provides the uniform decay rates for the energy function of the overall structure. The main novelty of this result, with respect to the literature, is that the uniform stability for the model is established without assuming any mechanical damping the wall.