Extended MPC for Closed-Loop re-identification based on probabilistic invariant sets

Recently, a Model Predictive Control (MPC) scheme suitable for closedloop re-identification was proposed which solves, in a non-conservative form, the potential conflict between the persistent excitation of the system and the stabilization. The idea is to use the concept of probabilistic invariance to define a target set, and so to take advantage of the knowledge of the probabilistic distribution of the excitation signal to design a non-competitive two-objective MPC formulation. Although this proposal seems to work properly from an identification point of view (since uncorrelated output-input data are obtained), some theoretical properties of the formulation remains unexploited. In this work, new results are presented, focusing on the finite-time convergence to the target, which is necessary to start the second MPC objective of identification. Furthermore, several new simulation are developed to clearly show the new properties benefits.