Abstract
In this paper, we study the quadratic optimal control problem on the half linet≥to, for nonautonomous control processes in Hilbert spaces. We prove that the quadratic optimal control problem has a solution if, and only if, an associated Riccati equation has a positive solution fort≥to. The optimal control is given in feedback form. If a detectability assumption holds, then we prove that the optimal control is a stabilizing feedback control when the associated Riccati equation has a positive solution which is bounded fort≥to.
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