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Stability of Evolving Fuzzy Systems based on Data Clouds

Research output: Contribution to journalJournal article

E-pub ahead of print
<mark>Journal publication date</mark>15/01/2018
<mark>Journal</mark>IEEE Transactions on Fuzzy Systems
<mark>State</mark>E-pub ahead of print
Early online date15/01/18
<mark>Original language</mark>English

Abstract

Evolving fuzzy systems (EFSs) are now well developed and widely used thanks to their ability to self-adapt both their structures and parameters online. Since the concept was firstly introduced two decades ago, many different types of EFSs have been successfully implemented. However, there are only very few works considering the stability of the EFSs, and these studies were limited to certain types of membership functions with specifically pre-defined parameters, which largely increases the complexity of the learning process. At the same time, stability analysis is of paramount importance for control applications and provides the theoretical guarantees for the convergence of the learning algorithms. In this paper, we introduce the stability proof of a class of EFSs based on data clouds, which are grounded at the AnYa type fuzzy systems and the recently introduced empirical data analysis (EDA) methodological framework. By employing data clouds, the class of EFSs of AnYa type considered in this work avoids the traditional way of defining membership functions for each input variable in an explicit manner and its learning process is entirely data-driven. The stability of the considered EFS of AnYa type is proven through the Lyapunov theory, and the proof of stability shows that the average identification error converges to a small neighborhood of zero. Although, the stability proof presented in this paper is specially elaborated for the considered EFS, it is also applicable to general EFSs. The proposed method is illustrated with Box-Jenkins gas furnace problem, one nonlinear system identification problem, Mackey-Glass time series prediction problem, eight real-world benchmark regression problems as well as a high frequency trading prediction problem. Compared with other EFSs, the numerical examples show that the considered EFS in this paper provides guaranteed stability as well as a better approximation accuracy.

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©2018 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.