Research On Fuzzy Control Of Nonlinear Systems

This thesis discusses several questions on fuzzy control, which content is divided into two parts. The first part studies the design methods of adaptive fuzzy regulator and controller of nonlinear systems, consisting of continuous-time system and discrete-time system; the second part studies the characteristic of fuzzy systems as the approximator of nonlinear systems.The main result is: (1) the design method of the adaptive fuzzy regulator is given, under the condition that the nonlinear function satisfies the boundedness or the linear increase in the system. The theoretical analysis shows that the two design methods can ensure the control law continuous and not produce the problem caused by sliding mode control. The global stability of the regulator is proved using the Lyapunov methods. (2) A new adaptive fuzzy control algorithm, which is different from the famous supervising control one is proposed for one kind of nonlinear system with disturbance. It is proven the algorithm ensures the boundedness of the tracking errors and global stability, using the adaptive law similar to thes -modifying method. (3) For a kind of general discrete nonlinear system, a new scheme of fuzzy adaptive controller with globally stability is proposed, based on new parameter adaptive law of the system. Owing to no need of the assumptions "x falling in a compact set" or "the base function being persistence excitation" which are difficult to be gotten and verified in reality, this result precedes the former research work. (4) The simulation results show that the control algorithms proposed in this paper are effective. (5)The constructively sufficient conditions of the approximating C1 functions and the explicit formula dealing with the approximation precision and the number of fuzzy rules are given for one kind of general fuzzy systems, using the methods different from the former ones which are based on the Stone-Weierstrass theory, therefore, the constructively sufficient conditions are also generalized from polynomial function to C1 function. The conservativeness of the sufficient condition given in the paper is less than before for polynomial function. (6) The number of fuzzy rules could directly be calculated and does not need be testified by using the formula proposed in the paper for multivariable polynomial function.