Abstract
In this note we consider a linear-quadratic time dependent control problem where the state end-points are constrained to affine varieties and where there is an affine pointwise state-control constraint. The problem is analyzed over a finite time interval. We characterize the existence of a unique solution by means of the existence of a solution of an associated Riccati equation. The optimal control solving the affine problem is expressed in a feed-back type form.
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