Adaptive Fuzzy Control For A Class Of Nonlinear System With Time-delay

The traditional control theory has been well developed until now. However, with the increasing of the control requirement, more and more complex problems in the control system have not been solved by the traditional control theory. The characteristics of these complex control systems are high nonlinearty, complicated control requirement, uncertainty etc. Thus mathematical model is hard to be established. The traditional adaptive techniques can only solve some relatively easy questions. Although, the fuzzy control theory has attracted more and more attention. The normal fuzzy control theory is hard to apply to the system with continuously changeable states. The application of the kind of fuzzy control is confined to some experiences. Therefore, fuzzy control with self-adaptability and self-learning should be introduced.In this thesis, the adaptive fuzzy control theory is studied and is applied to the nonlinear system with time-delay. First, the adaptive fuzzy control theory is analyzed. Then, based on TS model, a model of the nonlinear systems with time-delay is established. In the conclusion part of the TS model, the traditional fuzzy group is replaced with the linear and local equation. When the maximum defuzzification or center defuzzification is applied to solve the question, the conclusion values are constant. Thus, the TS model with fewer fuzzy rules can produce more complicated nonlinear functions and reduce the number of the fuzzy rules when solving the multi-variables systems. By making difference between the TS model and the estimation model with the same undetermined parameters, the final error model is derived. In order to make the error convergent to zero, the Lyapunov theory is used find the stability matrix, and then the Lyapunov function is obtained. To make the derivative of the Lyapunov function less than zero, the estimate model with unknown parameters is designed and the adaptive law is developed so that the state of the estimate model is gradually convergent to the state of the original model.