Identification of fuzzy prediction models through hyperellipsoidal clustering

A simplified ozone model based on fuzzy rules generation

“…The first and third quartiles are defined so that the first one is smaller than the third one. If two of them are equal, give one of them a small fluctuation to keep the restriction that qf 1 < qf 2 < qf 3 • The tuning parameters tf 1, tf 2 have default 1 and they are optimized in the identification of the fuzzy model (see Nakamori and Ryoke, 1994). Next, the membership function for Rule Rj is defined by 4 Jf(x) = ITJLik(xk;<f:1,<f:2 ,<f:3 ;lf1 ,lf2l· (5) k=l Estimation of ozj is done by the following formula: For a given x = (pvj 1 ,pvj 2 ,pvj3 ,pvj4) , …”

“…The subject of this paper is an alternative method of representing the results of the EMEP model as a response surface using fuzzy rule generation methodology (Nakamori and Ryoke, 1994). The idea is to construct a number of fuzzy rules about the source-receptor relationships between ozone precursor emissions and daily tropospheric ozone concentrations.…”

Decentralized adaptive fuzzy control of robot manipulators

“…Until now, a lot of efforts have been made to realize such features. To provide the fuzzy system with the first function abovementioned, Yamaguchi et al [11] and Nie et al [12] use BAM and CPN neural network, respectively, whilst Nakamori et al [13] select the clustering technique. As for the second function, backpropagation neural networks [14], pi-sigma neural network [15] and simulated annealing [16] are attempted for supervised parameter learning, while a neuron-like structure is used as reinforcement learning [17].…”

“…Given the desired trajectory and provided the feedforward torques are acceptably accurate, (12) can be linearized along the nominal trajectory (13) where and are the gradients of evaluated at and , respectively, , and and are the nominal values of and . Let and , then we have the following perturbation equation for the robot system: (14) As a result, the control problem reduces to producing a proper so that converges to zero.…”

“…However, if the uncertainties become unreasonably large, the controller will collapse. This can be explained that under such situations, the torques computed from the trained feedforward fuzzy systems are no longer near the nominal torques, and consequently, (13) does not hold.…”