Identification by Distributions of Continuous Time Systems with Nonlinear Feedback

This paper presents a procedure for the identification of continuous-time systems with memoryless nonlinear feedback. The feedback nonlinear element, described by a bounded unknown function, is expressed as a linear combination of some base functions. Both the parameters of the feedforward linear system and of the nonlinear element representation are identified. To improve the representation of the nonlinear functions, the set of basis functions is iteratively refined. It is possible to identify the dominant nonlinearities, applying the singular value decomposition to the input matrix. In our approach, the linear dynamic subsystem is described by a transfer function of a given order and the distribution based identification method is applied. The DCNFI (Distribution based of Continuous time Nonlinear Feedback Identification) equation is obtained. The consistency of the identification is analyzed and experimental results are presented. Key-Words: Identification, Nonlinear systems, Distributions.