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

By Cornelius T. Leondes

The publication emphasizes neural community constructions for attaining functional and potent structures, and offers many examples. Practitioners, researchers, and scholars in commercial, production, electric, mechanical,and creation engineering will locate this quantity a special and finished reference resource for varied program methodologies.Control and Dynamic platforms covers the $64000 subject matters of powerful Orthogonal Activation functionality established Neural community procedure structure, multi-layer recurrent neural networks for synthesizing and enforcing real-time linear control,adaptive keep an eye on of unknown nonlinear dynamical structures, optimum monitoring Neural Controller recommendations, a attention of unified approximation thought and functions, recommendations for the selection of multi-variable nonlinear version buildings for dynamic platforms with an in depth remedy of proper process version enter choice, excessive Order Neural Networks and Recurrent excessive Order Neural Networks, excessive Order second Neural Array platforms, on-line studying Neural community controllers, and Radial Bias functionality innovations. Key FeaturesCoverage includes:* Orthogonal Activation functionality dependent Neural community process structure (OAFNN)* Multilayer recurrent neural networks for synthesizing and enforcing real-time linear regulate* Adaptive keep an eye on of unknown nonlinear dynamical platforms* optimum monitoring Neural Controller concepts* attention of unified approximation conception and functions* suggestions for opting for multivariable nonlinear version constructions for dynamic platforms, with a close remedy of correct process version enter choice

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Sample text

The end effector uses a servo motor to adjust the position of a tool, based on the force sensor feedback, to compensate for force diversity. To design such an end effector, it is important to know the transfer function between the voltage to the servo amplifier and the end effector force. ~(t) Delta Rule ~(t) Delta Rule State Weights I ^C ^S ~VxOWxnWxn Transfer Function Estimator (~(jr Figure 10 ! ~ State Weights ^ ^c ^s W y0 W yn W yn I~(jco) = )~(jr Transfer function identification using the FSNN.

The relationship between the input Y = [Xl, x2 . . . ) is a complex harmonic function with the ~s as the state weights. The FSNN model defined by Eq. nm are trained to approach the coefficients of the Fourier series. nm --- [nlo)01 . . . nm and denotes the dot product operation of the two vectors. E. G R A D I E N T D E S C E N T L E A R N I N G A L G O R I T H M The learning in neural networks is performed by adapting the network weights (~s) such that the expected value of the mean squared error between network output and training output is minimized.

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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