Variable universe stable adaptive fuzzy control of a nonlinear system.

*(English)* Zbl 1045.93026
Summary: A kind of stable adaptive fuzzy control of a nonlinear system is implemented based on the variable universe method proposed first by *H.-X. Li* [“The mathematical essence of fuzzy controls and fine fuzzy controllers”, in: P. P. Wang (ed.), Advances in machine intelligence and soft computing. Vol. IV. Durham: Bookwrights Press, 55–74 (1997)]. 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 the literature. Second, it is proved that the variable universe adaptive fuzzy control is asymptotically stable by use of Lyapunov theory. The simulation on a second-order nonlinear system shows that its simulation effect is also quite good in comparison with the corresponding result of *L.-X. Wang* [“Stable adaptive fuzzy control of nonlinear systems”, IEEE Trans. Fuzzy Syst. 1, No. 2, 146–155 (1993)]. 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.

##### MSC:

93C42 | Fuzzy control systems |

93C10 | Nonlinear control systems |

93D20 | Asymptotic stability of control systems |