Abstract
We consider a control problem in a Banach space with a bounded observer, but an unbounded controller which takes values in the extrapolated Favard class. A least square regulator problem can be formulated if the observer and the admissible controls take values in Hilbert spaces. We prove that for this type of LQR-problem the value function is given by a Riccati operator, and that a bounded state feedback based on the Riccati operator yields the optimal control.
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