Stable Indirect Adaptive Type-2 Fuzzy Sliding Mode Control Using Lyapunov Approach

In this paper, a stable adaptive type-2 fuzzy tracking control equipped with sliding mode and Lyapunov synthesis approaches is proposed to attenuate the effects from unmodeled dynamics, external disturbance and approximation errors for nonlinear SISO systems. By employing adaptive fuzzy-neural control theory incorporated with Lyapunov stability criterion, the adaptive laws will be derived for approximating the uncertain nonlinear dynamical system. In comparison with conventional sliding model control and adaptive type-1 fuzzy control, the advocated approach not only guarantees closed-loop stability but also tracking performance of the overall system can be achieved without prior knowledge on the upper bound of the lumped uncertainty. Furthermore, chattering effect of the control input will be substantially reduced by the proposed technique. To validate the capability of the proposed approach, two examples, the inverted pendulum system and the vehicle active suspension system of a quarter-car, are given. Simulation results show that the interval type-2 fuzzy logic system can handle unpredicted internal disturbance and data uncertainties very well, but the conventional sliding mode controller and the adaptive type-1 fuzzy controller must expend more control effort in order to deal with noisy training data.