A note on the rates of uniform approximation of fuzzy systems

Abstract

For the fuzzy systems with the kernel-shaped fuzzy sets of if part, we estimate the rates of the uniform approximation for continuous functions. Results are given associatively with the rates of convergence of the sequence (log k/k) α .

Adaptive Fuzzy Control for Path Tracking of Underactuated Ships Based on Dynamic Equilibrium State Theory

“…So, the overlap region of fuzzy sets will not impact the performance of the controller. 17 The Gaussian membership function of fuzzy sets can be defined as 16 …”

“…Now, adaptive fuzzy control has been an effective control method for the uncertain nonlinear systems. [12][13][14][15][16][17] In view of this, this paper combines the DES tracking approach with adaptive fuzzy backstepping control method to obtain the desired path tracking of underactuated ships in presence of parameters variations and external disturbances caused by wind, wave and current. The proposed adaptive fuzzy controller guarantees the stability of the closed-loop system and achieves the good tracking performance as well.…”

Boundary value problem: Weak solutions induced by fuzzy partitions

“…Discussion. In the above given lemmas and theorems, we showed that the proposed finite dimensional spaces of test functions in the first and second particular sequences (12) and (13) approximate a certain infinite dimensional spaces of test functions in the sense of (5 ). The estimations of distances (14) and (29) coincide.…”

“…Recall that the ordinary theory of fuzzy transform (F-transform) was introduced by Perfilieva in [15] with the purpose to include fuzzy models into the approximation theory. At that time this idea was independently elaborated by many authors, and many interesting scientific paper appeared (see, e.g., [8,12]) where the most important fuzzy model, based on IF-THEN rules, was developed on a rigorous mathematical platform. However, only in [15], the development of fuzzy models was raised on the level of transforms, and the position of fuzzy modeling appeared in the same line with other classical (integral) transforms.…”

“…A uniform fuzzy partition can be characterized with the help of a kernel function, see e.g.,[8,12,18]. However, we prefer this notion due to its historical origin and because, this is the only connection with fuzzy modeling.…”