Design On Adaptive Fuzzy Controllers For Two Classes Of Nonlinear Systems

As an active research field, the nonlinear system theory made a rapid progress recently, especially in introducing differential geometry, which plays main important role in nonlinear system theory. The complex industry processes in varying operation conditions are often nonlinear and multi variable with uncertainties and strong coupling. So the exact mathematical model can not be determined with case. The foundation of fuzzy modeling and adaptive control of nonlinear systems is of artificial intelligence, which has the abilities such as self-studying and adaptive ability, automatic information processing ability to abate uncertainties and the programming ability to reliably complete control and can achieve effective control of the complex systems. Furthermore, the controller designed is easy in fuzzy control techniques, which is the same with many nonlinear systems and has strong robust characteristic. Since 80's 20th century, the fuzzy control obtains great development in control theory and engineering. In practice, it is very difficult to get the precise mathematical model from the traditional modeling method. Fuzzy systems with a collection of fuzzy IF-THEN rules are capable of approximating any real continous function on a compact set with arbitrary accuracy. Recently, fuzzy systems are successfully applied to many control problems because they need not accurate mathematical model of the system and can cooperate with human experts, knowledge. In addition, the recent study of adaptive fuzzy control has developed quickly. In many design problems, all states of systems are supposed to be available for measurement.The robust indirect adaptive fuzzy control methods are proposed for a class of nonlinear systems based on observer in this paper. The main content has two parts:In the first part, for a class of nonlinear system with disturbances, we design the state observer to estimate the unknown state and advance the scheme of robust indirect adaptive fuzzy making use of the H∞control theory and the characteristic of fuzzy logic is universal approximation. Finally, we prove that the states of the closed loop systems are uniformly bounded and the tracking error is attenuated to an arbitratily desired level via H∞tracking design technique. The main results are that (1) It is not required to assume that estimation error has a known boundary or satisfies square integral conditions and even it is not required that the states of the system are full observable. It is supposed that the boundary of estimation error and external disturbance are unknown. The online computational burden is greatly reduced since only uncertainty bounds are tuned online. (2) In the first part, we discuss the state observer can transform into tracking error observer and the parameters of adaptive law designed is simple but also bounded. The effect that function approximation error and the external disturbances have on the tracking error is compensated by means of the robust conortller designed. The presented scheme guarantees that H∞tracking performance is aehieved.In the second part, an adaptive robust fuzzy control method is proposed for a class of uncertain MIMO nonlinear systems with disturbances. we design the state observer to estimate the unknown state. The effect that function approximation error and the external disturbances have on the tracking error is compensated by means of the robust controller designed. For the case that the parameter adjustment of adaptive fuzzy control uses only the tracking error and leads to the low convergence rate of the tracking. The second part the adaptive law utilizes the tracking error and approximation error in the adaptive fuzzy control system. And the theory analysis and simulation results show that this method has better tracking performance, if co is square plot, this design not only tracking error converge to zero but also approximation error converge to zero. That is to say parameters of adaptive law converge to the optimal, so the adaptive robust fuzzy control can get the optimal control.