Indirect adaptive hierarchical fuzzy sliding mode controller for a class of nonlinear systems

This study presents a novel indirect adaptive hierarchical fuzzy sliding mode controller for a class of high-order SISO nonlinear systems in normal form with unknown functions in the presence of bounded disturbance. The hierarchical fuzzy system is able to reduce the number of rules and parameters with respect to ordinary fuzzy systems. On-line tuning algorithm for consequent part parameters of fuzzy rules in different layer of hierarchical fuzzy system is derived using defined Lyapunov function. Two theorems are proved to show that the suggested adaptive schemes can achieve asymptotically stable tracking of a reference input with guarantee of the bounded system signals. One for unity control gain and the other for non-unity control gain. To show the effectiveness of the proposed method, control of three systems are considered in the simulations. The simulations results demonstrate the validity, efficiency and feasibility of the proposed approach to control of nonlinear dynamic system.