Title: Recursive least squares algorithm and stochastic gradient algorithm for feedback nonlinear equation-error systems

Authors: Guanglei Song; Ling Xu; Feng Ding

Addresses: School of Mechanical Technology, Wuxi Institute of Technology, Wuxi, Jiangsu, China ' School of Internet of Things Technology, Wuxi Vocational Institute of Commerce, Wuxi, Jiangsu, China ' School of Internet of Things Engineering, Jiangnan University, Wuxi, Jiangsu, China

Abstract: Many industrial systems exhibit the nonlinear characteristics. Generally, the structure of the system is taken by feedback closed-loop for the purpose of realising the automatic control of industrial processes. Therefore, the industrial systems are the closed-loop feedback nonlinear systems which have complicated structures. The mathematical models of systems provide the support and basis for the design of the control system and the better control performance. However, it is hard to determine the models of closed-loop feedback nonlinear systems due to the complex structures. The goal of this study is to develop an identification way for a feedback nonlinear system including a forward channel and a feedback channel, where the forward channel is described by a controlled autoregressive model and the feedback channel takes the form of a static nonlinear function. By taking advantage of the least squares optimisation, a recursive least squares algorithm is established and shows its good performance to solve the identification problem for the feedback nonlinear system.

Keywords: parameter estimation; recursive identification; least squares; nonlinear system; feedback system.

DOI: 10.1504/IJMIC.2019.103666

International Journal of Modelling, Identification and Control, 2019 Vol.32 No.3/4, pp.251 - 257

Received: 12 Feb 2019
Accepted: 07 Mar 2019
Published online: 18 Nov 2019 *

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