Robust MPC suitable for closed-loop re-identification, based on probabilistic invariant sets

This work extends a recent set-based Model Predictive Control (MPC) scheme for closed loop reidentification that solves the potential conflict between the simultaneous persistent excitation of the system and the stabilization of the closed-loop system. Based on the original scheme proposed in González et al. (2014), this manuscript extends those results by taking into account model uncertainties and by exploiting the knowledge of the probability distribution of the excitation signal used to identify the plant. The robust extension solves the main drawback of the previous work, which was limited to a nominal analysis while the need of re-identification assumes the presence of model uncertainties. In addition, the probabilistic analysis allows the use of smaller target sets computed as Probabilistic Invariant Sets (PIS), improving the system performance during the identification procedure. Simulation results show the practical benefits of the novel robust strategy.