Advances and New Trends in Modeling and Control of Neural Network Models

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Network Science".

Deadline for manuscript submissions: closed (15 January 2021) | Viewed by 10894

Special Issue Editors


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Guest Editor
1. Department of Mathematical Physics, Technical University of Sofia, Sliven, Bulgaria
2. Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
Interests: nonlinear analysis; control theory; mathematical modeling; differential equations; fractional calculus
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Special Issue Information

Dear Colleagues,

Due to the impressive applications of neural network systems in significant fields in science and technology such as pattern recognition, associative memory, optimization, linear and nonlinear programing, and computer vision, the research on their fundamental and qualitative behavior has attracted the attention of a considerable audience of professionals. As a result, modeling, analysis, and control methods for neural network models have emerged as fundamental tools in pure and applied research. Additionally, the rapid development of large-scale computers and parallel computations has highly increased the industrial recognition of the use of neural network models for solving problems in technology as well as the number of strategies for their hardware implementation.

In this Special Issue, we provide an international forum for researchers to contribute original research focusing on the latest achievements and new trends in the modeling and control of neural network systems.

Prof. Dr. Gani Stamov
Dr. Ivanka Stamova
Guest Editors

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Keywords

  • Hopfield neural networks
  • Cellular neural networks
  • Bidirectional associative memory neural networks
  • Lotka–Volterra neural networks
  • Neural networks with delays
  • Impulsive neural networks
  • Cohen–Grossberg neural networks
  • Reaction–diffusion neural networks
  • Fractional neural networks
  • Stability
  • Periodicity
  • Almost periodicity
  • Modeling
  • Control
  • Stabilization
  • Applications in science and technology

Published Papers (5 papers)

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Research

20 pages, 958 KiB  
Article
High-Performance Tracking for Piezoelectric Actuators Using Super-Twisting Algorithm Based on Artificial Neural Networks
by Cristian Napole, Oscar Barambones, Mohamed Derbeli, Isidro Calvo, Mohammed Yousri Silaa and Javier Velasco
Mathematics 2021, 9(3), 244; https://doi.org/10.3390/math9030244 - 26 Jan 2021
Cited by 10 | Viewed by 2048
Abstract
Piezoelectric actuators (PEA) are frequently employed in applications where nano-Micr-odisplacement is required because of their high-precision performance. However, the positioning is affected substantially by the hysteresis which resembles in an nonlinear effect. In addition, hysteresis mathematical models own deficiencies that can influence on [...] Read more.
Piezoelectric actuators (PEA) are frequently employed in applications where nano-Micr-odisplacement is required because of their high-precision performance. However, the positioning is affected substantially by the hysteresis which resembles in an nonlinear effect. In addition, hysteresis mathematical models own deficiencies that can influence on the reference following performance. The objective of this study was to enhance the tracking accuracy of a commercial PEA stack actuator with the implementation of a novel approach which consists in the use of a Super-Twisting Algorithm (STA) combined with artificial neural networks (ANN). A Lyapunov stability proof is bestowed to explain the theoretical solution. Experimental results of the proposed method were compared with a proportional-integral-derivative (PID) controller. The outcomes in a real PEA reported that the novel structure is stable as it was proved theoretically, and the experiments provided a significant error reduction in contrast with the PID. Full article
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23 pages, 11115 KiB  
Article
Investigation of a Multitasking System for Automatic Ship Berthing in Marine Practice Based on an Integrated Neural Controller
by Van Suong Nguyen
Mathematics 2020, 8(7), 1167; https://doi.org/10.3390/math8071167 - 16 Jul 2020
Cited by 17 | Viewed by 2395
Abstract
In this article, a multitasking system is investigated for automatic ship berthing in marine practices, based on artificial neural networks (ANNs). First, a neural network with separate structures in hidden layers is developed, based on a head-up coordinate system. This network is trained [...] Read more.
In this article, a multitasking system is investigated for automatic ship berthing in marine practices, based on artificial neural networks (ANNs). First, a neural network with separate structures in hidden layers is developed, based on a head-up coordinate system. This network is trained once with the berthing data of a ship in an original port to conduct berthing tasks in different ports. Then, on the basis of the developed network, an integrated mechanism including three negative signs is linked to achieve an integrated neural controller. This controller can bring the ship to a berth on each side of the ship in different ports. The whole system has the ability to berth for different tasks without retraining the neural network. Finally, to validate the effectiveness of the proposed system for automatic ship berthing, numerical simulations were performed for berthing tasks, such as different ports, and berthing each side of the ship. The results indicate that the proposed system shows a good performance in automatic ship berthing. Full article
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17 pages, 701 KiB  
Article
Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays
by Călin-Adrian Popa and Eva Kaslik
Mathematics 2020, 8(7), 1146; https://doi.org/10.3390/math8071146 - 13 Jul 2020
Cited by 12 | Viewed by 2331
Abstract
This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state [...] Read more.
This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control scheme is employed to realize the finite-time Mittag–Leffler synchronization of these networks by using the fractional-order extension of the Lyapunov direct method for Mittag–Leffler stability. Two numerical examples illustrate the feasibility and the effectiveness of the deduced sufficient criteria. Full article
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18 pages, 282 KiB  
Article
Global Stability of Integral Manifolds for Reaction–Diffusion Delayed Neural Networks of Cohen–Grossberg-Type under Variable Impulsive Perturbations
by Gani Stamov, Ivanka Stamova, George Venkov, Trayan Stamov and Cvetelina Spirova
Mathematics 2020, 8(7), 1082; https://doi.org/10.3390/math8071082 - 03 Jul 2020
Cited by 10 | Viewed by 1475
Abstract
The present paper introduces the concept of integral manifolds for a class of delayed impulsive neural networks of Cohen–Grossberg-type with reaction–diffusion terms. We establish new existence and boundedness results for general types of integral manifolds with respect to the system under consideration. Based [...] Read more.
The present paper introduces the concept of integral manifolds for a class of delayed impulsive neural networks of Cohen–Grossberg-type with reaction–diffusion terms. We establish new existence and boundedness results for general types of integral manifolds with respect to the system under consideration. Based on the Lyapunov functions technique and Poincarѐ-type inequality some new global stability criteria are also proposed in our research. In addition, we consider the case when the impulsive jumps are not realized at fixed instants. Instead, we investigate a system under variable impulsive perturbations. Finally, examples are given to demonstrate the efficiency and applicability of the obtained results. Full article
14 pages, 279 KiB  
Article
On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays
by Gani Stamov, Ivanka Stamova, Stanislav Simeonov and Ivan Torlakov
Mathematics 2020, 8(3), 335; https://doi.org/10.3390/math8030335 - 03 Mar 2020
Cited by 10 | Viewed by 1884
Abstract
The present paper is devoted to Bidirectional Associative Memory (BAM) Cohen–Grossberg-type impulsive neural networks with time-varying delays. Instead of impulsive discontinuities at fixed moments of time, we consider variable impulsive perturbations. The stability with respect to manifolds notion is introduced for the neural [...] Read more.
The present paper is devoted to Bidirectional Associative Memory (BAM) Cohen–Grossberg-type impulsive neural networks with time-varying delays. Instead of impulsive discontinuities at fixed moments of time, we consider variable impulsive perturbations. The stability with respect to manifolds notion is introduced for the neural network model under consideration. By means of the Lyapunov function method sufficient conditions that guarantee the stability properties of solutions are established. Two examples are presented to show the validity of the proposed stability criteria. Full article
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