Modeling of Dynamic Systems Using Orthogonal Endocrine Adaptive Neuro-Fuzzy Inference Systems

Abstract

This paper presents a new method for designing adaptive neuro-fuzzy inference systems (ANFIS). Improvements are made by introducing specially developed orthogonal functions into the very structure of ANFIS, specifically, into the layer that imitates Sugeno stile defuzzification. These functions are specially tailored for analysis and synthesis of dynamic systems and they also contain an adaptive measure of the variability of the systems operating in a real environment, which can be implemented inside the ANFIS as hormonal effect.

Orthogonal Hybrid-Fuzzy Controllers

“…This servo system [18,20], beside hardware, includes open-architecture software that extends the MATLAB environment for real-time control experiments. The servo system setup consists of several modules (DC motor, brass inertia, backlash, encoder, magnetic brake, gearbox with the output disc) arranged in the chain, mounted at the metal rail and coupled with the small clutches.…”

“…RTDAC/USB acquisition board with A/D converters is used for all the measurements whereby all the functions of the board can be accessed from the Modular Servo Toolbox. The model of the system which is considered is linear because of ignoring effect of dry friction as well as effect of saturation [18][19][20].…”

A New Class of Cascade Orthogonal Filters based on a Special Inner Product with Application in Modeling of Dynamical Systems

“…In the case of modeling a particular unknown system, parameters of the model should be adjusted in such a way that the model in Figure 9 corresponds as closely as possible to the unknown system. The process of modeling is performed in the well-known manner by introducing the same input to the system itself, as well as to its adjustable model based on the new cascade orthogonal digital filter ( Figure 10) [15,17,18,20]. The genetic algorithm used in the experiment has same values for initial population, the number of generations like in previous one, and reproduction with six elite individuals.…”

“…The method is based on the pole-zero and zero-pole mapping by using symmetric transformation. In this way obtained rational functions were used to design of new classes of orthogonal filters, quazi-orthogonal filters [15], almost orthogonal filters [16][17][18][19][20][21] and finally, generalized orthogonal filters with complex poles [22]. Using the same method, new classes of Malmquist orthogonal functions can also be obtained.…”

Generalized Quasi-Orthogonal Polynomials Applied in Sliding Mode-based Minimum Variance Control of ABS

“…On the other hand, the signals generated by the generalized quasi-orthogonal filters of k-th order can be successfully applied as the activation functions of neural networks [22,24]. Moreover, it has been shown in [26] that these functions can replace the functions inside the layer that imitates Sugeno style defuzzification in the traditional ANFIS network. In [27], it has been already proved that orthogonal models, obtained by almost orthogonal filters, can be very effective for the design of SMC in the continuous-time domain.…”