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 isconsidered. The control operator is assumed to be unbounded on thespace of finite energy (for the so-called boundary or pointcontrol problems). A numerical algorithm (based on FEM methods) forcomputations of discrete solutions to Algebraic Riccati Equations(ARE) is formulated.It is shown that the proposed algorithm provides strongly convergentsolutions of the ARE. As the result, the convergence of optimal solutions as well as the associatedperformance index is established.

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