In this paper, the attention is focused on the tracking of a piecewise constant reference for an LTI system in presence of state-control constraints and bounded disturbance inputs. Exploiting robust controlled invariant sets in the extended state-setpoint space, we propose a novel predictive tracking algorithm which yields robust constraint satisfaction and good tracking performance with a reasonable on-line computational burden. The main idea is to adopt a dual-mode controller that operates as a predictive regulator whenever the desired setpoint is feasible or in feasibility recovery mode otherwise. Simulation results demonstrate the improved tracking performance of the proposed method with respect to available techniques.