Sliding Mode Control of a Class of Uncertain Nonlinear Time-Delay Systems Using LMI and TS Recurrent Fuzzy Neural Network

Tung-Sheng CHIANG  Chian-Song CHIU 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E92-A  No.1  pp.252-262
Publication Date: 2009/01/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Systems and Control
Keyword: 
sliding mode control,  FNN,  time delay,  linear matrix inequality (LMI), 

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Summary: 
This paper proposes the sliding mode control using LMI techniques and adaptive recurrent fuzzy neural network (RFNN) for a class of uncertain nonlinear time-delay systems. First, a novel TS recurrent fuzzy neural network (TS-RFNN) is developed to provide more flexible and powerful compensation of system uncertainty. Then, the TS-RFNN based sliding model control is proposed for uncertain time-delay systems. In detail, sliding surface design is derived to cope with the non-Isidori-Bynes canonical form of dynamics, unknown delay time, and mismatched uncertainties. Based on the Lyapunov-Krasoviskii method, the asymptotic stability condition of the sliding motion is formulated into solving a Linear Matrix Inequality (LMI) problem which is independent on the time-varying delay. Furthermore, the input coupling uncertainty is also taken into our consideration. The overall controlled system achieves asymptotic stability even if considering poor modeling. The contributions include: i) asymptotic sliding surface is designed from solving a simple and legible delay-independent LMI; and ii) the TS-RFNN is more realizable (due to fewer fuzzy rules being used). Finally, simulation results demonstrate the validity of the proposed control scheme.