Identification and control of nonlinear system based on Laguerre-ELM Wiener model

• An Laguerre-ELM Wiener model is proposed for identifying and control of nonlinear dynamic system.
• The order of linear part of Laguerre-ELM Wiener model is determined using Lipschitz quotient criterion.
• The parameters of Laguerre-ELM are estimated using generalized ELM algorithm.
• GPC control scheme of nonlinear system based on Laguerre-ELM model is proposed.

In this paper, a new Wiener model is presented for identification and control of single-input single-output (SISO) nonlinear systems. The proposed Wiener model consists of a linear Laguerre filter in cascaded with an extreme learning machine (ELM) neural network (called Laguerre-ELM Wiener model). Laguerre filter can approximate a stable linear system to any degree of accuracy with a small number of Laguerre filters, which provides a parsimony structure and high level accuracy simultaneously. To determine the appropriated number of Laguerre filters in Laguerre-ELM Wiener model, Lipschitz quotient criterion is adapted to determine the order of linear part. A generalized ELM algorithm is proposed to estimate the parameters of Laguerre-ELM Wiener model. Once the unknown nonlinear system is identified using Laguerre-ELM Wiener model, a generalized predictive control (GPC) algorithm is designed for control of nonlinear system. The advantage of the proposed control method is that it transfers a nonlinear control problem to a linear one by inserting the inverse of static nonlinear section. Simulation results demonstrate the effectiveness of the proposed identification and control algorithms.