Identification of feedback nonlinear systems with unknown time-delay and orders

An identification algorithm based on extended basis pursuit de-noising iteration is proposed for feedback nonlinear systems with unknown time-delay in the forward channel and unknown system orders. Firstly, an identification model of the closed-loop system is established based on the input data and the output data of the feedback nonlinear block. Secondly, considering the unknown time-delay and orders in the forward channel by designing polynomials with sufficiently high orders based on the over-parametrization method, a high dimensional sparse vector with a sparsity equal to the number of parameters to be identified is obtained. Then, in order to solve the problem that forward channel output terms and noise terms in the information vector are unmeasurable, the approach taken here is to replace the unknown terms with estimated outputs and estimated residuals, respectively. Finally, based on the over-parameterization model and the basis pursuit de-noising algorithm, an extended basis pursuit de-noising iterative algorithm is proposed to estimate the unknown parameters, orders, and time-delay of the feedback nonlinear systems. A simulation example is given to demonstrate the effectiveness of the proposed algorithm.