This paper investigates the constrained infinite horizon linear quadratic regulator (CIHLQR). In particular, it is shown that the terminal set inclusion condition that is associated with this control law introduces limitations into the control system. By relaxing this condition it is demonstrated that the resulting controller will in many cases remain equivalent to CIHLQR. It is further shown that CIHLQR with a relaxed terminal set inclusion condition offers significant benefits, in terms of computational expense and performance when compared with standard finite horizon model predictive control (MPC) approaches. (C) 2004 Elsevier Ltd. All rights reserved.