We study finite horizon optimal control where the controller is subject to sensor-information constraints, that is, each input has access to a fixed subset of states at all times. In particular, we consider linear systems affected by exogenous disturbances with state and input constraints. We establish the class of sensor-information structures that allows for the formulation of this optimization problem as a convex program. In the literature, Quadratic Invariance (QI) is a well-established result that is applicable to the infinite horizon unconstrained case. We show that, despite state and inputs constraints being enforced, QI results can be naturally adapted to our problem. To this end, we highlight and exploit the connection between Youla parametrization and disturbance-feedback policies. Additionally, we provide graph-theoretic visual insight which is consistent with Partially Nested (PN) interpretations.