Fuzzy Adaptive Stabilization And Tracking Control For Nonlinear Uncertainty Systems Based On Partion Of Unity

The control design for most nonlinear systems is based on the accurate mathematical models. However, it is difficult to obtain the accurate information of controlled object. In general, the controlled systems possess uncertainly nonlinear property and operate under disturbances, such as structural uncertainty, parameter uncertainty and exogenous disturbances. These uncertainties and disturbances bring in variance between the practical systems and their mathematical models, and ultimately worsen the systems performance. Therefore it is extremely important to design controllers for nonlinear systems with uncertainties in real applications.Combining adaptive control, fuzzy control and Backstepping technique, this thesis focuses attention on the adaptive stabilization and tracking control problem of nonlinear uncertain systems based on the method of partition of unity. Compared to some existent results, the control methods in this thesis not only show the approximate capacity of the partition of unity but also reduce the number of adaptive laws. The main work and research results of this thesis lie in the following aspects:(1) An adaptive tracking control is developed for a class of nonlinear system. In the control design, partition of unity is used to approximate the controllers. The results show that the tracking errors converge to a small neighborhood of zero and states in the closed-loop system are bounded via the controllers. The developed design scheme is applied to design tracking controller for Duffing Forced Oscillation System. Simulation result demonstrates the effectiveness of the proposed scheme.(2) By utilizing the property that partition of unity can approximate any continuous functions on the compact set at arbitrary precision, the robust tracking controllers with PI structure and adaptive laws are designed for a class of uncertain nonlinear system with large and fast disturbances. The results show that the tracking errors converge to zero and all states in the closed-loop systems are bounded via the controllers. Numerical simulations are given to illustrate the validity of the proposed method. (3) A robust adaptive controller by using the Backstepping technique and the partition of unity method is proposed. At first, we use the partition of unity method to approximate the nonlinear uncertainties. Second, the smooth extension robust compensators are applied to suppress the partition of unity approximation errors. Meanwhile, the filter signals are employed to circumvent algebraic loop problems. By using suitable partition of unity, the proposed adaptive controllers in this paper guarantee that all the states of the closed-loop systems are uniformly ultimately bounded (UUB) as well as require fewer restrictive assumptions. A numerical example demonstrates the effectiveness of the proposed approach.(4) A novel adaptive controller based on partition of unity is presented for a class of strict-feedback nonlinear system. The partition of unity is used to approximate the uncertainties and a systematic design procedure is developed for synthesis of adaptive control which includes the Backstepping technique. The method preserves the main advantage is that the adaptive mechanism with only one learning parameter is obtained. The developed design scheme is applied to design tracking controller for Brusselator model and one-link robot manipulator. Simulation results demonstrate the effectiveness of the proposed scheme.(5) A novel adaptive EPU method stabilization control design scheme has been proposed for n order nonlinear system. The proposed method not only efficiently reduces the number of adaptive laws but also relaxes the restriction on universal approximators, whose output usually needs to be linear combination of basis functions in control design. The EPU has been proved with good approximation accuracy by tuning the scalar factor. Compared with the existing results, the main advantage of our result is different kinds of universal approxiamtors such as PU, neural network, fuzzy logic system, fuzzy logic system without rule bases, can use to approximate the nonlinear terms. Meanwhile, the adaptive laws have nothing to do with basis functions. Via variable structure method the controllers are designed in two cases:(i) If the states of controlled systems (SSs) increase in large ratio with time, the size of parameters of the scalars (SPS) increases by updated laws and the controllers are placed out of service, so that the systems is an open-loop. Increasing the SPS ensures that the SSs can go into the effective range of the saturator; (ii) If SSs go into the effective range of the saturator, the SPS decreases by the updated laws and the adaptive controller with EPU guarantees the states of the system controlled converge to a small region near the origin, so that the system is a closed-loop. At last, a comparison of the numerical example is given to illustrate the effectiveness of the approach.(6) A novel adaptive FWR stabilization control design scheme has been proposed for n order nonlinear system with scalars and saturators. The main advantages of this method are that the adaptive laws have nothing to do with fuzzy basis functions, because the proposed adaptive laws just use to tuning approximation accuracies of FWR, Lipschitz constants and scalar factor, and the FWR is benefit to control multiple variables systems. Compared with chapter 6, in this section, the unknown nonlinear functions just only satisfy continuous property on the compact set, which extends the applicability of the approach to different kinds of practice systems. Finally, a comparison of the numerical example is given to illustrate the effectiveness of the approach.This work was supported by the National Natural Science Foundation of Guangdong Province (No.8151009001000061), (No.10151009001000039), Team Project of the Guangdong Natural Science Foundation (No.8351009001000002).