Convergence of Numerical Algorithms for the Approximations to Riccati Equations Arising in Smart Material Acoustic Structure Interactions

An optimal control problem governed by a coupled hyperbolic-parabolic like dynamics arising in structural acoustic problems is considered. The control operator is assumed to be unbounded on the space of finite energy (for the so-called boundary or point control problems). A numerical algorithm (based on FEM methods) for computations of discrete solutions to Algebraic Riccati Equations (ARE) is formulated. It is shown that the proposed algorithm provides strongly convergent solutions of the ARE. As the result, the convergence of optimal solutions as well as the associated performance index is established