Variable universe stable adaptive fuzzy control of a nonlinear system

A kind of stable adaptive fuzzy control of a nonlinear system is implemented based on the variable universe method proposed first in [1]. First of all, the basic structure of variable universe adaptive fuzzy controllers is briefly introduced. Then the contraction-expansion factor which is a key tool of the variable universe method is defined by means of the integral regulation idea, and then a kind of adaptive fuzzy controller is designed by using such a contraction-expansion factor. The simulation on the first-order nonlinear system is done, and as a result, its simulation effect is quite good in comparison with the corresponding result in [2,3]. Second, it is proved that the variable universe adaptive fuzzy control is asymptotically stable by use of Liapunov theory. The simulation on a second-order nonlinear system shows that its simulation effect is also quite good in comparison with the corresponding result in [2]. Besides, a useful tool, called symbolic factor, is proposed, which may be of universal significance. It can greatly reduce the setting time and enhance the robustness of the system.