A Set Membership approach to the identification of linear systems with guaranteed simulation accuracy

Marco Lauricella

Politecnico di Milano, Italy

Thursday, February 07, 2019, 14:00

Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany

The identification of models of linear systems having guaranteed simulation accuracy is of great importance in all the cases where a model and a measure of its uncertainty are needed for long range prediction or simulation purpose, like in robust Model Predictive Control. In this talk, I will address the problem of model identification for linear systems affected by a bounded additive disturbance, where the bound is unknown, and a finite set of sampled data is available for model identification. The objective is the identification of one-step-ahead models, and the estimation of their accuracy by means of worst-case simulation error bounds, resorting to the Set Membership identification framework. I will present new results that allow to develop a procedure for the estimation of the unknown disturbance bound and of the system decay rate from data. Then, the available data and the estimated disturbance bound are used to define the set of all the possible models that are compatible with data and with the estimated quantities. The estimated decay rate is used to refine the standard Feasible Parameter Set (FPS) formulation, by adding constraints that enforce a converging behavior of the iterated models. Finally, the desired one-step-ahead model is identified by numerical optimization, and the worst-case error bound related to the obtained model is calculated over the available data and FPSs. The performance and the validity of the proposed approach are evaluated over numerical simulations and a real world experimental case study.