Control and Dynamic Systems (Neural Network Systems by Cornelius T. Leondes

By Cornelius T. Leondes

The e-book emphasizes neural community buildings for reaching sensible and powerful structures, and gives many examples. Practitioners, researchers, and scholars in business, production, electric, mechanical,and construction engineering will locate this quantity a different and finished reference resource for various software methodologies.Control and Dynamic platforms covers the $64000 issues of powerful Orthogonal Activation functionality dependent Neural community process structure, multi-layer recurrent neural networks for synthesizing and enforcing real-time linear control,adaptive keep watch over of unknown nonlinear dynamical platforms, optimum monitoring Neural Controller recommendations, a attention of unified approximation concept and functions, strategies for the decision of multi-variable nonlinear version constructions for dynamic structures with a close remedy of suitable approach version enter decision, excessive Order Neural Networks and Recurrent excessive Order Neural Networks, excessive Order second Neural Array structures, on-line studying Neural community controllers, and Radial Bias functionality thoughts. Key FeaturesCoverage includes:* Orthogonal Activation functionality dependent Neural community approach structure (OAFNN)* Multilayer recurrent neural networks for synthesizing and imposing real-time linear keep watch over* Adaptive keep watch over of unknown nonlinear dynamical structures* optimum monitoring Neural Controller suggestions* attention of unified approximation thought and purposes* suggestions for deciding upon multivariable nonlinear version constructions for dynamic structures, with an in depth therapy of suitable approach version enter choice

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By Cornelius T. Leondes

The e-book emphasizes neural community buildings for reaching sensible and powerful structures, and gives many examples. Practitioners, researchers, and scholars in business, production, electric, mechanical,and construction engineering will locate this quantity a different and finished reference resource for various software methodologies.Control and Dynamic platforms covers the $64000 issues of powerful Orthogonal Activation functionality dependent Neural community process structure, multi-layer recurrent neural networks for synthesizing and enforcing real-time linear control,adaptive keep watch over of unknown nonlinear dynamical platforms, optimum monitoring Neural Controller recommendations, a attention of unified approximation concept and functions, strategies for the decision of multi-variable nonlinear version constructions for dynamic structures with a close remedy of suitable approach version enter decision, excessive Order Neural Networks and Recurrent excessive Order Neural Networks, excessive Order second Neural Array structures, on-line studying Neural community controllers, and Radial Bias functionality thoughts. Key FeaturesCoverage includes:* Orthogonal Activation functionality dependent Neural community approach structure (OAFNN)* Multilayer recurrent neural networks for synthesizing and imposing real-time linear keep watch over* Adaptive keep watch over of unknown nonlinear dynamical structures* optimum monitoring Neural Controller suggestions* attention of unified approximation thought and purposes* suggestions for deciding upon multivariable nonlinear version constructions for dynamic structures, with an in depth therapy of suitable approach version enter choice

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Additional resources for Control and Dynamic Systems (Neural Network Systems Techniques and Applications)

Example text

091 was employed to train Legendre, harmonic, and polynomial networks, whereas the true gradient descent learning algorithm with adaptive learning rate and momentum was used for faster learning Of the sigmoid network. The sigmoid network weights were initialized based on Nguyen-Widrow random weight generation algorithm for better performance. 0001 per cycle or 500 training cycles were completed. The approximation errors for the four networks are shown in Fig. 7. 005). Figure 8 shows the training error for all four networks.

The frequency weights in a FSNN can be determined using only one parameter, which is the base frequency ~o0i = 2 p / T i , because the frequency weight sequence is an arithmetic series. The period T/should equal the period of the corresponding system input variable xi if xi is periodic, or equal the range of the variable xi if xi is nonperiodic. One important variation of the FSNN design is based on the possibility of using only cosine or sine activation functions to simulate cosine or sine half range expansion of the Fourier series.

L : : " Flai'rhofiib " [ . . . ~ . I - - Legendre - ................................ 5 ~ ............. / L .................................. -2 /' \. 04 1-". . . . . . . . 06 ;' ...... 'i .............. -/- . . . . . 'h<. 05. 7"\i ................. o2 _i. / _L_. 5 I f - - - Pb[yhb/nial 1 . . . -. ,~.... I..... I 1 ! 5 I 2 Figure 7 Function approximation error. polynomial and sigmoid networks. 0018, but took 500 cycles to reach this error level as compared to 36 cycles taken by the Legendre network to reach a comparable error level.

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