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This paper presents a novel set-based model predictive control for tracking,which provides the largest domain of attraction, even with the minimalpredictive/control horizon. The formulation - which consists of a singleoptimization problem - shows a dual behavior: one operating inside the maximalcontrollable set to the feasible equilibrium set, and the other operating atthe N-controllable set to the same equilibrium set. Based on some finite-timeconvergence results, asymptotic stability of the resulting closed-loop isproved, while recursive feasibility is ensured for any change of the setpoint.The properties and advantages of the proposal have been tested on simulationmodels.

Set-based MPC for discrete-time LTI systems with maximal domain of attraction and minimal predictive control horizon