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This paper presents a novel tracking predictive controller for constrained nonlinear systems capable to deal with sudden and large variations of a piece-wise constant setpoint signal. The uncertain nature of the setpoint may lead to stability and feasibility issues if a regulation predictive controller based on the stabilizing terminal constraint is used. The tracking model predictive controller presented in this paper extends the MPC for tracking for constrained linear systems to the more complex case of constrained nonlinear systems. The key idea is the addition of an artificial reference as a new decision variable. The considered cost function penalizes the deviation of the predicted trajectory with respect to the artificial reference as well as the distance between the artificial reference and the setpoint. Closed-loop stability and recursive feasibility for any setpoint are guaranteed, thanks to an appropriate terminal cost and extended stabilizing terminal constraint. Also, two simplified formulations are shown: the design based on a terminal equality constraint and the design without terminal constraint. The resulting controller ensures recursive feasibility for any changing setpoint. In the case of unreachable setpoints, asymptotic stability of the optimal reachable setpoint is also proved. The properties of the controller have been tested on a constrained continuous stirred tank reactor simulation model and have been experimentally validated on a four-tanks plant. Index Terms-Model predictive control, nonlinear systems, setpoint tracking. I. INTRODUCTION M ODEL predictive control (MPC) is one of the most successful advanced control techniques in the process industry. Its properties have been widely investigated in the last two decades and currently the MPC is a control technique capable to provide stability, robustness, constraint satisfaction,

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In this paper, a robust MPC for constrained discrete-time nonlinear system with additive uncertainties is presented. This controller uses a terminal cost, a terminal constraint and nominal predictions. The terminal region and the constraints on the states are computed to get robust feasibility of the closed loop system for a given bound on the admissible uncertainties. Furthermore, it is proved that the closed-loop system is input-to-state stable with relation to the uncertainties. Therefore, the closed-loop system evolves towards a compact set where it is ultimately bounded. In case of decaying uncertainties, the closed-loop system is asymptotically stable. The convergence of the closed loop system is guaranteed despite the suboptimality of the solution.

The closed loop formulation of the robust MPC has been shown to be a control technique capable of robustly stabilize uncertain nonlinear systems subject to constraints. Robust asymptotic stability of these controllers has been proved when the uncertainties are decaying. In this paper we extend the existing results to the case of uncertainties that decay with the state but do not tend to zero. This allows us to consider both plant uncertainties and external disturbances in a less conservative way.First, we provide some results on robust stability under the considered kind of uncertainties. Based on these, we prove robust stability of the min-max MPC. In the paper we show how the robust design of the local controller is translated to the min-max controller and how the persistent term of the uncertainties determines the convergence rate of the closed-loop system.

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