Model predictive control suitable for closed-loop re-identification

•A new MPC suitable for closed-loop re-identification is proposed.•A re-identification needs to be developed in a closed-loop fashion, since the process cannot be stopped.•The main problem is the conflict between the control and identification objectives.•A generalization, from punctual stability to (invariant) set stability, is done to avoid the conflict.•The proposal could be potentially applied to real processes.

The main problem of a closed-loop re-identification procedure is that, in general, the dynamic control and identification objectives are conflicting. In fact, to perform a suitable identification, a persistent excitation of the system is needed, while the control objective is to stabilize the system at a given equilibrium point. However, a generalization of the concept of stability, from punctual stability to (invariant) set stability, allows for a flexibility that can be used to avoid the conflict between these objectives. Taking into account that an invariant target set includes not only a stationary component, but also a transient one, the system could be excited without deteriorating the stability of the closed-loop. In this work, a MPC controller is proposed that ensures the stability of invariant sets at the same time that a signal suitable for closed-loop re-identification is generated. Several simulation results show the propose controller formulation properties.