Study Of Type-2 Fuzzy Control Methods With Active Adaptivity

For a complex nonlinear system susceptible to external disturbance, how to design an effective controller, which can eliminate the influence of all kinds of disturbance factors, ensure robustness and stability of the system, is an important hot issue in the field of control science. The difficulties lie in that the complex system's high degree of uncertainty, which leads to the inability to establish an accurate model.At the same time, the internal perturbation of the system and the perturbation of the external environment will affect the control stability and convergence effect. In order to put forward new methods and ideas for solving the nonlinear system control problem, Type-2 fuzzy control methods with active adaptivity are established by integrating the biological initiative adjustment and adaptive behaviors to the external disturbances and internal disturbances into the controller design in this paper. The main research contents are as follows:(1) Regard the main ecological factors of biological individuals as variables of rule antecedent in Type-2 fuzzy system. The fuzzy sets of these variables are Type-2 fuzzy sets. The "broadband" effect of Type-2 fuzzy membership function can reflect the '“ecological amplitude" of biological ecological factors. Regard the “ecostate" and"ecorole" in the functional niche as parameters of the fuzzy rule consequent. Based on the niche "ecostate-ecorole" theory,"ecostate" reflect individual survival status and"ecorole" reflect individual development trend. So, the resulting Type-2 T-S fuzzy system has the biological coping mechanism of the external disturbances, which improves the system ability to describe the uncertainty, strengthens the actual relationship between the rule antecedent and rule consequent of T-S fuzzy system, and gives the fuzzy system the function of the active adapting, regulating, developing and utilizing to the environment similar to biological organisms.(2) For two different types of control systems, using the Type-2 fuzzy systems with active adaptability to model the unknown function of the control system, direct adaptive Type-2 fuzzy control method and indirect adaptive Type-2 fuzzy control method with active adaptivity are respectively established based on the classical adaptive Type-2 fuzzy control method. Using Lyapunov synthesis method, the adaptive law and constraint condition of system parameters are given. The stability of the closed-loop system under the uniformly boundness of all variables is studied, and the convergence of the control system is analyzed. This method combines the bio-intelligent characteristics of active adapting to environment and the advantages to solve the problem with high degree of uncertainties of the Type-2 fuzzy system theory.The simulation results show that the proposed controller can make the system variables have less fluctuation and faster convergence under the random disturbance by using less fuzzy rules. That is, the designed control method integrating biological characteristics is better superior in control effect.(3) In the case that the state variables of control system are not measurable,direct adaptive and indirect adaptive Type-2 fuzzy observer control method with active adaptivity are established by using Type-2 T-S fuzzy system with active adaptivity to design fuzzy observer. The proposed methods can improve the tracking precision of the controlled object by online adjustment of the adaptive law. It makes the system have many characteristics of dealing with uncertainties, which is more effective in dealing with unknown disturbance and training noise. Using the Lyapunov synthesis method, the stability of the closed-loop system under the uniformly boundness of all variables is studied by adding a robust controller and a nonlinear combination controller for observing errors. Furthermore, the adaptive laws and constraints of the system parameters are given and the convergence of the system is analyzed. The simulation results show that the controller can achieve very obvious control effect under a few fuzzy rules, and the designed new controller has strong anti-interference ability.(4) By combining the Type-2 T-S fuzzy system with active adaptivity with the fuzzy sliding-mode controller design, Type-2 fuzzy sliding-mode control method with active adaptivity is established. By using the method of Lyapunov synthesis, the stability of closed-loop systems with uniform boundness of all variables is studied.And the adaptive law and constraint conditions of the system parameters are given. As a result of the integrating of the biological active adaptation strategy to the Environment, the proposed control method has strong anti-interference ability and can effectively alleviate the chattering phenomena appearing in the classic sliding-mode control system. The simulation results show that the designed Type-2 fuzzy sliding mode control method has stronger ability to deal with unknown disturbances than the Type-1 fuzzy control method.In summary,using the biological "ecostate" and "ecorole" in the functional niche,which reflect the biological active adaptivity, Type-2 T-S fuzzy system rule and Type-2 adaptive fuzzy control methods with active adaptivity are designed in this paper. The proposed new methods not only retain the control performance of conventional adaptive fuzzy control methods, but also effectively improve the system robustness to disturbance and uncertain factors, as well as the system convergence, so that the system has active adaptivity and better stability.