Theoretical Analyses of the Universal Approximation Capability of a Class of Higher Order Neural Networks Based on Approximate Identity

2016 ◽  
pp. 1456-1470 ◽  
Author(s):  
Saeed Panahian Fard ◽  
Zarita Zainuddin
Keyword(s):  
Neural Networks ◽  
Approximation Theory ◽  
Special Class ◽  
Higher Order ◽  
Approximate Identity ◽  
Universal Approximation ◽  
Multivariate Functions ◽  
Higher Order Neural Networks ◽  
Approximation Capability ◽  
Theoretical Analyses

One of the most important problems in the theory of approximation functions by means of neural networks is universal approximation capability of neural networks. In this study, we investigate the theoretical analyses of the universal approximation capability of a special class of three layer feedforward higher order neural networks based on the concept of approximate identity in the space of continuous multivariate functions. Moreover, we present theoretical analyses of the universal approximation capability of the networks in the spaces of Lebesgue integrable multivariate functions. The methods used in proving our results are based on the concepts of convolution and epsilon-net. The obtained results can be seen as an attempt towards the development of approximation theory by means of neural networks.

Theoretical Analyses of the Universal Approximation Capability of a class of Higher Order Neural Networks based on Approximate Identity

2016 ◽  
pp. 192-207
Author(s):  
Saeed Panahian ◽  
Zarita Zainuddin
Keyword(s):  
Neural Networks ◽  
Approximation Theory ◽  
Special Class ◽  
Higher Order ◽  
Approximate Identity ◽  
Universal Approximation ◽  
Multivariate Functions ◽  
Higher Order Neural Networks ◽  
Approximation Capability ◽  
Theoretical Analyses

One of the most important problems in the theory of approximation functions by means of neural networks is universal approximation capability of neural networks. In this study, we investigate the theoretical analyses of the universal approximation capability of a special class of three layer feedforward higher order neural networks based on the concept of approximate identity in the space of continuous multivariate functions. Moreover, we present theoretical analyses of the universal approximation capability of the networks in the spaces of Lebesgue integrable multivariate functions. The methods used in proving our results are based on the concepts of convolution and epsilon-net. The obtained results can be seen as an attempt towards the development of approximation theory by means of neural networks.

Robust Adaptive Control Using Higher Order Neural Networks and Projection

2010 ◽  
pp. 99-137 ◽  
Author(s):  
Wen Yu
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Dead Zone ◽  
Higher Order ◽  
Robust Adaptive Control ◽  
On Line ◽  
The Neural Networks ◽  
Higher Order Neural Networks ◽  
Robust Adaptive ◽  
Approximation Capability

By using dynamic higher order neural networks, we present a novel robust adaptive approach for a class of unknown nonlinear systems. Firstly, the neural networks are designed to identify the nonlinear systems. Dead-zone and projection techniques are applied to weights training, in order to avoid singular cases. Secondly, a linearization controller is proposed based on the neuro identifier. Since the approximation capability of the neural networks is limited, four types of compensators are addressed. We also proposed a robust neuro-observer, which has an extended Luenberger structure. Its weights are learned on-line by a new adaptive gradient-like technique. The control scheme is based on the proposed neuro-observer. The final structure is composed by two parts: the neuro-observer and the tracking controller. The simulations of a two-link robot show the effectiveness of the proposed algorithm.

Artificial Tactile Sensing and Robotic Surgery Using Higher Order Neural Networks

2010 ◽  
pp. 514-544 ◽  
Author(s):  
Siamak Najarian ◽  
Sayyed Mohsen Hosseini ◽  
Mehdi Fallahnezhad
Keyword(s):  
Neural Networks ◽  
Medical Instrument ◽  
Research Work ◽  
Higher Order ◽  
Ann Model ◽  
Nonlinear Input ◽  
Higher Order Neural Networks ◽  
Sense Of Touch ◽  
Theoretical Analyses ◽  
Theoretical Results

In this chapter, a new medical instrument, namely, the Tactile Tumor Detector (TTD) able to simulate the sense of touch in clinical and surgical applications is introduced. All theoretical and experimental attempts for its construction are presented. Theoretical analyses are mostly based on finite element method (FEM), artificial neural networks (ANN), and higher order neural networks (HONN). The TTD is used for detecting abnormal masses in biological tissue, specifically for breast examinations. We also present a research work on ANN and HONN done on the theoretical results of the TTD to reduce the subjectivity of estimation in diagnosing tumor characteristics. We used HONN as a stronger open box intelligent unit than traditional black box neural networks (NN) for estimating the characteristics of tumor and tissue. The results show that by having an HONN model of our nonlinear input-output mapping, there are many advantages compared with ANN model, including faster running for new data, lesser RMS error and better fitting properties.

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