Fuzzy Modeling of Non-Uniformly Sampling Nonlinear Systems Based on Clustering Method and Convergence Analysis
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Fuzzy Modeling of Non-Uniformly Sampling Nonlinear Systems Based on Clustering Method and Convergence Analysis∗ WANG Hongwei · XIE Lirong
DOI: 10.1007/s11424-020-9119-7 Received: 10 April 2019 / Revised: 22 August 2019 c The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2020 Abstract The studying motivation of this paper is that there exist many modeling issues of nonuniformly sampling nonlinear systems in industrial systems. Based on multi-model modeling principle, the corresponding model of non-uniformly sampling nonlinear systems is described by the nonlinear weighted combination of some linear models at local working points. Fuzzy modeling based on multimodel scheme is a common method to describe the dynamic process of non-linear systems. In this paper, the fuzzy modeling method of non-uniformly sampling nonlinear systems is studied. The premise structure of the fuzzy model is confirmed by GK fuzzy clustering, and the conclusion parameters of the fuzzy model are estimated by the recursive least squared algorithm. The convergence perfromance of the proposed identification algorithm is given by using lemmas and martingale theorem. Finally, the simulation example is given to demonstrate the effectiveness of the proposed method. Keywords tems.
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Convergence analysis, fuzzy modeling, nonlinear systems, non-uniformly sampling sys-
Introduction
Conventional discrete-time sampling systems, also known as single-rate systems, assume that the control updating period is equal to the output sampling period, and the updating process of the input signals and the sampling process of the output signals are operated simultaneously. Identification and control of such single-rate systems have been fully investigated, with equidistant sampling intervals for each variable. There are many systems with more than WANG Hongwei School of Electrical Engineering, Xinjiang University, Urumqi 830047, China; School of Control Science and Control Engineering, Dalian University of Technology, Dalian 116024, China. Email: [email protected]. XIE Lirong School of Electrical Engineering, Xinjiang University, Urumqi 830047, China. ∗ The research was supported by the National Natural Science Foundation of China under Grant Nos. 61863034 and 51667021. This paper was recommended for publication by Editor FENG Gang.
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WANG HONGWEI · XIE LIRONG
one operation frequency in industrial processes, i.e., multirate systems. There are a lot of multirate systems in process industries, such as polymer reactors, where the liquid composition, density and molecular weight distribution are manually measured, while the manipulated variables may be updated at relatively faster rates. In multirate sampling systems, there is also a class of non-uniformly sampling systems (NUSS). For non-uniformly sampling systems, many researchers are interested in the broad fields, including identification, filtering, signal process, fault diagnosis, control, and so on. At present, the research methods on system identification, signal filtering, signal process, fault diagnosi
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