Adaptive Fuzzy Control For Affine Nonlinear Systems

In adaptive fuzzy control researches, the direct and indirect adaptive fuzzy control approaches are frequently used in many schemes which only utilize the knowledge of control behavior or plant. The knowledge of human experience or experts, however, can not be used sufficiently. Moreover, most methods are designed under the assumption that approximation error is squared integral or the supermom of the optimal approximation error is known. Besides, adaptive parameterθis only adjusted by tracking error e(t), without considering the influence of approximation errorε(t).Based on the above problems, the main research works in this paper are stated as follows:(1) A stable combined adaptive fuzzy control method based on the observer is proposed for a class of SISO uncertain affine nonlinear system. The knowledge of control behavior and plant can be used sufficiently in this scheme. The adaptive compensation term of the optimal approximation error is adopted. The approach does not require the optimal approximation error is squared integral or the supermom of the optimal approximation error is known. What's more, the adaptive law utilizes two types of errors in the adaptive fuzzy systems, the tracking error and approximation error. Based on Lyapunov stability theory, it is proved that all variables in the closed-loop system are bounded and tracking error converges to a neighborhood of zero. Through the simulation results, the effectiveness of the approach is demonstrated.(2) A new approach about adaptive fuzzy control based on the observer is proposed for a class of MIMO affine unobservable nonlinear systems. By applying the concept of "dominant input", the adaptive compensation term of the optimal approximation error is adopted. The approach does not require the optimal approximation error is squared integral or the supermom of the optimal approximation error is known. What's more, the adaptive law utilizes two types of errors in the adaptive fuzzy systems, the tracking error and approximation error. All signals in the closed-loop systems are bounded and tracking error converges to a neighborhood of zero. Through the simulation results, the effectiveness of the approach is demonstrated.