Adaptive TS-FNN control for a class of uncertain multi-time-delay systems: The exponentially stable sliding mode-based approach

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 (C) 2008 John Wiley & Sons, Ltd.