Probabilistic Invariant Sets for Closed-Loop Re-Identification

Recently, a Model Predictive Control (MPC) suitable for closed-loop re-identification was proposed, which solves the potential conflict between the persistent excitation of the system and the stabilization of the closed-loop by extending the equilibrium-point-stability to the invariant-set-stability. The proposed objective set, however, derives in large regions that contain conservatively the excited system evolution. In this work, based on the concept of probabilistic invariant sets, the controller target sets are substantially reduced ensuring the invariance with a sufficiently large probability (instead of deterministically), giving the resulting MPC controller the necessary flexibility to be applied in a wide range of systems.