Adaptive Control Of Uncertain Systems Based On Generalized Fuzzy Hyperbolic Model

With the rapid pace of science and technology, the development of industrial enginee-ring system turn towards a highly complex and intelligent trend, which requires the fuzzy c-ontrol theory continued development. In order to ensure system’s stability, traditional fuzzy adaptive control will choose a larger compact set to control the system’s state variable, but leading to a number of fuzzy rules increasing exponentially. At the same time,The online adjustment calculation of adaptive control law will also be greatly increased, which seriou-sly affects the control speed and effect. In order to meet the needs of actual production and practice, generalized fuzzy hyperbolic model (GFHM) comes into being. Because it is easier to describe and access,with lower number of fuzzy rules,GFHM is widely apply in the unce-rtainty system study.Therefore, based on GFHM.the uncertainty system study has attracted more and more scholars.In this paper, a adaptive control algorithm based on GFHM is proposed for nonlinear system with external disturbances. Combining the backstepping technique, the controller is designed and achieve the control objectives. Details as follows:Firstly, it briefly introduce the uncertain system, backstepping technique and GFHM adaptive control and its research status at domestic and foreign.Secondly, the basic mathematic definitions and relevant theorems are introduced.prim-arily includes, the basic principle of fuzzy control, fuzzy logic systems, the definition of G-FHM and its approximation properties and characteristics. For brevity, this article only foc-uses on introducing the Lyapunov stability theory.Lastly, to overcome the uncertainties for a class of nonlinear system with external dis-turbances, an adaptive control scheme is proposed. The proposed scheme is taking advanta-ge of the property of the GFHM with a universal approximator, high precision identification and a lower number of fuzzy rules. Furthermore, the system controller is designed by comb-ining the backstepping technique and makes the state of the system ultimately uniformly bo-unded.Next, the boundedness of closed-loop system’s all signals is proved by Lyapunov sta-bility theory. Finally, the simulation examples show that the proposed scheme is better appr- oximation effects than traditional adaptive fuzzy control...