Nonlinear MPC for tracking piece-wise constant reference signals

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.