AbstractIn this paper the relations between the finite horizon optimal control problem with receding horizon and the infinite horizon problem are discussed; the system is assumed to be linear, time‐invariant, and stabilizable. The cost function is quadratic but the output in the integral of the cost function may be undetectable. Control problems with terminal cost and problems with linear terminal state constraints are dealt with. The solution of the infinite horizon problem as well as the limiting behaviour of the solution of the finite horizon problem are derived. A necessary and sufficient condition for equivalence is developed; it is satisfied for the standard linear regulator proble