This paper is concerned with the explicit solution to constrained receding-horizon reference tracking control problems. The goal of this work is, for any scalar reference trajectory, to find the optimal control law for SISO linear systems such that a quadratic cost functional is minimised over a horizon of length N, subject to the satisfaction of input constraints, and under the assumption that the reference is known over the entire horizon. A global solution (i.e., valid in the entire data-space) for this problem, and for arbitrary horizon N, is derived analytically by using dynamic programming. The optimal solution is given by a piece-wise affine function of the data (the initial state of the system and the reference sequence), and the data-space is partitioned into a number of polyhedral regions, inside each of which a unique affine function is applied. From the dynamic programming solution, a clear relationship is exposed between input-constrained reference tracking problems and state estimation problems in the presence of constrained disturbances.
CDC-ECC '05: 44th IEEE Conference on Decision and Control, 2005 and European Control Conference 2005. Proceedings of The 44th IEEE Conference on Decision and Control 2005 and European Control Conference 2005 (Seville, Spain 12-15 December, 2005) p. 1701-1706