Optimal MPC for tracking constrained linear systems

Model predictive control (MPC) is one of the few techniques which is able to handlewith constraints on both state and input of the plant. The admissible evolution and asymptoticconvergence of the closed loop system is ensured by means of suitable choice of the terminalcost and terminal constraint. However, most of the existing results on MPC are designedfor a regulation problem. If the desired steady state changes, the MPC controller must beredesigned to guarantee the feasibility of the optimization problem, the admissible evolutionas well as the asymptotic stability. Recently, a novel MPC has been proposed to ensure thefeasibility of the optimization problem, constraints satisfaction and asymptotic evolution ofthe system to any admissible target steady-state.A drawback of this controller is the lost of a desirable property of the MPC controllers:the local optimality property. In this paper, a novel formulation of the MPC for trackingis proposed aimed to recover the optimality property maintaining all the properties of theoriginal formulation.