In 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 problem.
KEY WORDS Linear-quadratic optimal regulator Linear systems Riccati equations Geometric methods However, in many practical applications the length t , of the time interval [O, tl] is artificial. To avoid this problem an infinite time interval is considered: t , + 00. Then the problem statement is to control system (l), minimizing limt, r](t,). In most textbooks the infinite time interval problem is analysed as the limiting case of the finite time problem for increasing t , . More explicitly, this leads to the consideration of the following two problems: