Adaptive variable structure hierarchical fuzzy control for a class of high-order nonlinear dynamic systems.

In this paper, a novel adaptive hierarchical fuzzy control system based on the variable structure control is developed for a class of SISO canonical nonlinear systems in the presence of bounded disturbances. It is assumed that nonlinear functions of the systems be completely unknown. Switching surfaces are incorporated into the hierarchical fuzzy control scheme to ensure the system stability. A fuzzy soft switching system decides the operation area of the hierarchical fuzzy control and variable structure control systems. All the nonlinearly appeared parameters of conclusion parts of fuzzy blocks located in different layers of the hierarchical fuzzy control system are adjusted through adaptation laws deduced from the defined Lyapunov function. The proposed hierarchical fuzzy control system reduces the number of rules and consequently the number of tunable parameters with respect to the ordinary fuzzy control system. Global boundedness of the overall adaptive system and the desired precision are achieved using the proposed adaptive control system. In this study, an adaptive hierarchical fuzzy system is used for two objectives; it can be as a function approximator or a control system based on an intelligent-classic approach. Three theorems are proven to investigate the stability of the nonlinear dynamic systems. The important point about the proposed theorems is that they can be applied not only to hierarchical fuzzy controllers with different structures of hierarchical fuzzy controller, but also to ordinary fuzzy controllers. Therefore, the proposed algorithm is more general. To show the effectiveness of the proposed method four systems (two mechanical, one mathematical and one chaotic) are considered in simulations. Simulation results demonstrate the validity, efficiency and feasibility of the proposed approach to control of nonlinear dynamic systems.