Optimal MPC for tracking of constrained linear systems

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Model predictive control (MPC) is one of the few techniques which is able to handle constraints on both state and input of the plant. The admissible evolution and asymptotic convergence of the closed-loop system is ensured by means of suitable choice of the terminal cost and terminal constraint. However, most of the existing results on MPC are designed for a regulation problem. If the desired steady-state changes, the MPC controller must be redesigned to guarantee the feasibility of the optimisation problem, the admissible evolution as well as the asymptotic stability. Recently, a novel MPC has been proposed to ensure the feasibility of the optimisation problem, constraints satisfaction and asymptotic evolution of the system to any admissible target steady-state. A drawback of this controller is the loss of a desirable property of the MPC controllers: the local optimality property. In this article, a novel formulation of the MPC for tracking is proposed aimed to recover the optimality property maintaining all the properties of the original formulation. 1. Introduction Model predictive control (MPC) is one of the most successful techniques of advanced control in the process industry. This is due to its control problem formulation, the natural usage of the model to predict the expected evolution of the plant, the optimal character of the solution and the explicit consideration of hard constraints in the optimisation problem. Thanks to the recent developments of the underlying theoretical framework, MPC has become a mature control technique capable to provide controllers ensuring stability, robustness, constraint satisfaction and tractable computation for linear and for non-linear systems (Camacho and Bordons 2004). The control law is calculated by predicting the evolution of the system and computing the admissible sequence of control inputs which makes the system evolves …