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Adaptive TS‐FNN control for a class of uncertain multi‐time‐delay systems: The exponentially stable sliding mode‐based approach
Author(s) -
Chiang TungSheng,
Chiu ChianSong,
Liu Peter
Publication year - 2009
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.1052
Subject(s) - control theory (sociology) , exponential stability , fuzzy logic , artificial neural network , nonlinear system , fuzzy control system , mathematics , stability (learning theory) , computer science , control (management) , artificial intelligence , machine learning , physics , quantum mechanics
This paper presents an adaptive Takagi–Sugeno fuzzy neural network (TS‐FNN) control for a class of multiple time‐delay uncertain nonlinear systems. First, we develop a sliding surface guaranteed to achieve exponential stability while considering mismatched uncertainty and unknown delays. This exponential stability result based on a novel Lyapunov–Krasovskii method is an improvement when compared with traditional schemes where only asymptotic stability is achieved. The stability analysis is transformed into a linear matrix inequalities problem independent of time delays. Then, a sliding mode control‐based TS‐FNN control scheme is proposed to achieve asymptotic stability for the controlled system. Since the TS‐FNN combines TS fuzzy rules and a neural network structure, fewer numbers of fuzzy rules and tuning parameters are used compared with the traditional pure TS fuzzy approach. Moreover, all the fuzzy membership functions are tuned on‐line even in the presence of input uncertainty. Finally, simulation results show the control performance of the proposed scheme. Copyright © 2008 John Wiley & Sons, Ltd.