scholarly journals Piecewise Convex Technique for the Stability Analysis of Delayed Neural Network

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Zixin Liu ◽  
Jian Yu ◽  
Daoyun Xu ◽  
Dingtao Peng
Keyword(s):  
Neural Network ◽  
Time Delays ◽  
Convex Combination ◽  
Uncertain System ◽  
Activation Function ◽  
Positive Matrix ◽  
Neuron Activation ◽  
Delayed Neural Network ◽  
The Stability ◽  
Delay Partitioning

On the basis of the fact that the neuron activation function is sector bounded, this paper transforms the researched original delayed neural network into a linear uncertain system. Combined with delay partitioning technique, by using the convex combination between decomposed time delay and positive matrix, this paper constructs a novel Lyapunov function to derive new less conservative stability criteria. The benefit of the method used in this paper is that it can utilize more information on slope of the activations and time delays. To illustrate the effectiveness of the new established stable criteria, one numerical example and an application example are proposed to compare with some recent results.

STABILITY AND BIFURCATION ANALYSIS ON A DELAYED NEURAL NETWORK MODEL

2005 ◽  
Vol 15 (09) ◽  
pp. 2883-2893 ◽  
Author(s):  
XIULING LI ◽  
JUNJIE WEI
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Network Model ◽  
Neural Network Model ◽  
Center Manifold ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
Delayed Neural Network ◽  
The Stability

A simple delayed neural network model with four neurons is considered. Linear stability of the model is investigated by analyzing the associated characteristic equation. It is found that Hopf bifurcation occurs when the sum of four delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. An example is given and numerical simulations are performed to illustrate the obtained results. Meanwhile, the bifurcation set is provided in the appropriate parameter plane.

scholarly journals Memristor Based Binary Convolutional Neural Network Architecture With Configurable Neurons

2021 ◽  
Vol 15 ◽  
Author(s):  
Lixing Huang ◽  
Jietao Diao ◽  
Hongshan Nie ◽  
Wei Wang ◽  
Zhiwei Li ◽  
...  
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
High Precision ◽  
Network Architecture ◽  
Large Scale ◽  
Network Performance ◽  
Recognition Accuracy ◽  
Activation Function ◽  
Data Set ◽  
Neuron Activation

The memristor-based convolutional neural network (CNN) gives full play to the advantages of memristive devices, such as low power consumption, high integration density, and strong network recognition capability. Consequently, it is very suitable for building a wearable embedded application system and has broad application prospects in image classification, speech recognition, and other fields. However, limited by the manufacturing process of memristive devices, high-precision weight devices are currently difficult to be applied in large-scale. In the same time, high-precision neuron activation function also further increases the complexity of network hardware implementation. In response to this, this paper proposes a configurable full-binary convolutional neural network (CFB-CNN) architecture, whose inputs, weights, and neurons are all binary values. The neurons are proportionally configured to two modes for different non-ideal situations. The architecture performance is verified based on the MNIST data set, and the influence of device yield and resistance fluctuations under different neuron configurations on network performance is also analyzed. The results show that the recognition accuracy of the 2-layer network is about 98.2%. When the yield rate is about 64% and the hidden neuron mode is configured as −1 and +1, namely ±1 MD, the CFB-CNN architecture achieves about 91.28% recognition accuracy. Whereas the resistance variation is about 26% and the hidden neuron mode configuration is 0 and 1, namely 01 MD, the CFB-CNN architecture gains about 93.43% recognition accuracy. Furthermore, memristors have been demonstrated as one of the most promising devices in neuromorphic computing for its synaptic plasticity. Therefore, the CFB-CNN architecture based on memristor is SNN-compatible, which is verified using the number of pulses to encode pixel values in this paper.

Dynamical Effects of Neuron Activation Gradient on Hopfield Neural Network: Numerical Analyses and Hardware Experiments

2019 ◽  
Vol 29 (04) ◽  
pp. 1930010 ◽  
Author(s):  
Bocheng Bao ◽  
Chengjie Chen ◽  
Han Bao ◽  
Xi Zhang ◽  
Quan Xu ◽  
...  
Keyword(s):  
Neural Network ◽  
Control Parameter ◽  
Period Doubling ◽  
Response Speed ◽  
Hopfield Neural Network ◽  
Activation Function ◽  
Numerical Analyses ◽  
Dynamical Behaviors ◽  
Neuron Activation ◽  
Crisis Scenarios

Hyperbolic tangent function, a bounded monotone differentiable function, is usually taken as a neuron activation function, whose activation gradient, i.e. gain scaling parameter, can reflect the response speed in the neuronal electrical activities. However, the previously published literatures have not yet paid attention to the dynamical effects of the neuron activation gradient on Hopfield neural network (HNN). Taking the neuron activation gradient as an adjustable control parameter, dynamical behaviors with the variation of the control parameter are investigated through stability analyses of the equilibrium states, numerical analyses of the mathematical model, and experimental measurements on a hardware level. The results demonstrate that complex dynamical behaviors associated with the neuron activation gradient emerge in the HNN model, including coexisting limit cycle oscillations, coexisting chaotic spiral attractors, chaotic double scrolls, forward and reverse period-doubling cascades, and crisis scenarios, which are effectively confirmed by neuron activation gradient-dependent local attraction basins and parameter-space plots as well. Additionally, the experimentally measured results have nice consistency to numerical simulations.

scholarly journals A Compound Controller of an Aerial Manipulator Based on Maxout Fuzzy Neural Network

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xinchen Qi ◽  
Jianwei Wu ◽  
Jiansheng Pan
Keyword(s):  
Neural Network ◽  
Fuzzy Neural Network ◽  
Fuzzy Theory ◽  
Activation Function ◽  
Attitude Error ◽  
The Neural Network ◽  
Aerial Manipulator ◽  
Fuzzy Neural ◽  
Neural Network Algorithm ◽  
The Stability

The aerial manipulator is a complex system with high coupling and instability. The motion of the robotic arm will affect the self-stabilizing accuracy of the unmanned aerial vehicles (UAVs). To enhance the stability of the aerial manipulator, a composite controller combining conventional proportion integration differentiation (PID) control, fuzzy theory, and neural network algorithm is proposed. By blurring the attitude error signal of UAV as the input of the neural network, the anti-interference ability and stability of UAV is improved. At the same time, a neural network model identifier based on Maxout activation function is built to realize accurate recognition of the controlled model. The simulation results show that, compared with the conventional PID controller, the composite controller combined with fuzzy neural network can improve the anti-interference ability and stability of UAV greatly.

A NEURAL NETWORK CONTROLLER FOR THE PATH TRACKING CONTROL OF A HOPPING ROBOT INVOLVING TIME DELAYS

2006 ◽  
Vol 16 (01) ◽  
pp. 47-62 ◽  
Author(s):  
V. SREE KRISHNA CHAITANYA ◽  
M. SRINIVAS REDDY
Keyword(s):  
Neural Network ◽  
Time Delays ◽  
Vital Role ◽  
Tracking Performance ◽  
Robot Dynamics ◽  
Neural Network Controller ◽  
Hopping Robot ◽  
The Neural Network ◽  
Highly Nonlinear ◽  
The Stability

In this paper a hopping robot motion with offset mass is discussed. A mathematical model has been considered and an efficient single layered neural network has been developed to suit to the dynamics of the hopping robot, which ensures guaranteed tracking performance leading to the stability of the otherwise unstable system. The neural network takes advantage of the robot regressor dynamics that expresses the highly nonlinear robot dynamics in a linear form in terms of the known and unknown robot parameters. Time delays in the control mechanism play a vital role in the motion of hopping robots. The present work also enables us to estimate the maximum time delay admissible with out losing the guaranteed tracking performance. Further this neural network does not require offline training procedures. The salient features are highlighted by appropriate simulations.

scholarly journals Analysis and control of the fractional chaotic Hopfield neural network

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Emad E. Mahmoud ◽  
Lone Seth Jahanzaib ◽  
Pushali Trikha ◽  
Omar A. Almaghrabi
Keyword(s):  
Neural Network ◽  
Bifurcation Analysis ◽  
Chaos Control ◽  
Hopfield Neural Network ◽  
Activation Function ◽  
Neuron Activation ◽  
Long Time ◽  
Uniqueness Of The Solution ◽  
And Control ◽  
Adaptive Smc

AbstractThe fractional Hopfield neural network (HNN) model is studied here analyzing its symmetry, uniqueness of the solution, dissipativity, fixed points etc. A Lyapunov and bifurcation analysis of the system is done for specific as well as variable fractional order. Since a very long time ago, HNN has been carefully studied and applied in various fields. Because of the exceptional non-linearity of the neuron activation function, the HNN system is stoutly non-linear. Chaos control using adaptive SMC considering disturbances and uncertainties is done about randomly chosen points by designing suitable controllers. Numerical simulations performed in MATLAB verify the efficacy of the designed controllers.

scholarly journals Dynamics in a Delayed Neural Network Model of Two Neurons with Inertial Coupling

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Changjin Xu ◽  
Peiluan Li
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Neural Network Model ◽  
Center Manifold ◽  
Explicit Formulas ◽  
Normal Form Theory ◽  
Inertial Coupling ◽  
Form Theory ◽  
Delayed Neural Network ◽  
The Stability

A delayed neural network model of two neurons with inertial coupling is dealt with in this paper. The stability is investigated and Hopf bifurcation is demonstrated. Applying the normal form theory and the center manifold argument, we derive the explicit formulas for determining the properties of the bifurcating periodic solutions. An illustrative example is given to demonstrate the effectiveness of the obtained results.

SCORING MODELING BASED ON NEURAL NETWORKS FOR DETERMINING A BANK BORROWER'S RATING

2020 ◽  
Vol 2020 (10) ◽  
pp. 54-62
Author(s):  
Oleksii VASYLIEV ◽  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Statistical Data ◽  
Activation Function ◽  
Decision Making Process ◽  
Neural Network Architecture ◽  
Acceptable Accuracy ◽  
The Neural Network ◽  
Sigmoid Activation Function

The problem of applying neural networks to calculate ratings used in banking in the decision-making process on granting or not granting loans to borrowers is considered. The task is to determine the rating function of the borrower based on a set of statistical data on the effectiveness of loans provided by the bank. When constructing a regression model to calculate the rating function, it is necessary to know its general form. If so, the task is to calculate the parameters that are included in the expression for the rating function. In contrast to this approach, in the case of using neural networks, there is no need to specify the general form for the rating function. Instead, certain neural network architecture is chosen and parameters are calculated for it on the basis of statistical data. Importantly, the same neural network architecture can be used to process different sets of statistical data. The disadvantages of using neural networks include the need to calculate a large number of parameters. There is also no universal algorithm that would determine the optimal neural network architecture. As an example of the use of neural networks to determine the borrower's rating, a model system is considered, in which the borrower's rating is determined by a known non-analytical rating function. A neural network with two inner layers, which contain, respectively, three and two neurons and have a sigmoid activation function, is used for modeling. It is shown that the use of the neural network allows restoring the borrower's rating function with quite acceptable accuracy.

scholarly journals Data-Driven Stability Assessment of Multilayer Long Short-Term Memory Networks

2021 ◽  
Vol 11 (4) ◽  
pp. 1829
Author(s):  
Davide Grande ◽  
Catherine A. Harris ◽  
Giles Thomas ◽  
Enrico Anderlini
Keyword(s):  
Neural Network ◽  
Network Architecture ◽  
Short Term Memory ◽  
Moving Average ◽  
Machine Learning Algorithms ◽  
Physical Models ◽  
Data Driven ◽  
The Stability ◽  
And Control ◽  
Nonlinear Autoregressive

Recurrent Neural Networks (RNNs) are increasingly being used for model identification, forecasting and control. When identifying physical models with unknown mathematical knowledge of the system, Nonlinear AutoRegressive models with eXogenous inputs (NARX) or Nonlinear AutoRegressive Moving-Average models with eXogenous inputs (NARMAX) methods are typically used. In the context of data-driven control, machine learning algorithms are proven to have comparable performances to advanced control techniques, but lack the properties of the traditional stability theory. This paper illustrates a method to prove a posteriori the stability of a generic neural network, showing its application to the state-of-the-art RNN architecture. The presented method relies on identifying the poles associated with the network designed starting from the input/output data. Providing a framework to guarantee the stability of any neural network architecture combined with the generalisability properties and applicability to different fields can significantly broaden their use in dynamic systems modelling and control.

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