A Novel Identification Method for a Class of Closed-Loop Systems Based on Basis Pursuit De-Noising

This paper presents a novel method to identify a class of closed-loop systems, in which both the forward channel and the feedback channel have unknown time-delays. Taking into account the time-delays, an overparameterized identification model with a sparse parameter vector is established. Based on the basis pursuit de-noising criterion, the sparse parameter vector is estimated by solving a quadratic programming. The time-delays and the parameters are estimated according to the structure of the parameter estimation vector and the model equivalence principle, respectively. The proposed method is applicable even in the case of a few number of sampled data. The effectiveness of the proposed algorithm is verified by the numerical simulation results.