Abstract
The linear quadratic control problem for systems governed by evolution equations of parabolic type is considered. The optimal feedback control uses a Riccati operator which is approximated by a Galerkin scheme. Optimal convergence rates (except for a logarithmic factor) are derived for the approximation of the Riccati operator for both the finite and infinite time interval. This is done in an abstract Hilbert space framework assuming a certain rate of convergence for the uncontrolled system. In the numerical part, the Galerkin method is compared with the collocation method with special emphasis on the feedback gains.
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