Nonlinear MPC for Tracking Piecewise-Constant Reference Signals: the Positive Semidefinite Stage Cost Case

Model Predictive Control (MPC) is a successful control strategy, with solid theoretical and practical backgrounds. Currently, several stabilizing MPC formulations are available to deal with tracking of piecewise constant references. In particular, it is well understood that, in many cases, the use of artificial reference variables in the optimisation problem allows to sensibly extend the region of attraction of the controller. This work proposes a modified MPC for tracking formulation which is able to guarantee nominal stability also in presence of positive semidefinite stage cost. This can be particularly useful when dealing with high order and/or black-box models, as it allows penalizing the outputs or a subset of states of the system without compromising stability. The algorithm design is based on terminal ingredients and a cost detectability assumption which is explicitly accounted for in the algorithm formulation. Such assumption can be verified by means of input-output-to-state stability arguments, as well as dissipativity ones, thus exploiting techniques already available in the literature.