Interval type-2 fuzzy-neuro control of nonlinear systems with proved overall system stability

In this paper, we put forward an interval type-2 fuzzy neural network (IT2FNN) to deal with control issues of nonlinear systems with uncertainties. The fuzzy rules of the IT2FNN use interval type-2 triangular fuzzy sets to account for antecedent parts and adopt crisp numbers for the corresponding consequents. To effectively cope with uncertainties in the systems, a sliding-mode-control theory-based approach with new parameter learning rules is proposed to update the IT2FNN. The overall stability of the proposed methodology is also proved by using appropriate Lyapunov functions. Finally, the proposed method is applied to control the angular position of an inverted pendulum system. Simulation results indicate that, compared to a conventional proportional-derivative controller, the IT2FNN with the proposed learning rules can eliminate the uncertainties in performance and efficiently track the angle trajectory as desired.