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Artificial Neural Networks and Dynamic Control Systems
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Artificial Neural Networks and Dynamic Control Systems

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

Deadline for manuscript submissions: 31 May 2024 | Viewed by 6422

Special Issue Editors

Prof. Dr. P. Balasubramaniam

E-Mail Website1 Website2
Guest Editor
Department of Mathematics, The Gandhigram Rural Institute-Deemed to be University, Gandhigram 624 302, India
Interests: differential equations; stability analysis of neural networks; control theory; optimal control; fuzzy logic and its applications; image processing; cryptography
Dr. R. Vijay Aravind

E-Mail Website
Guest Editor
Research Center for Complex Systems, Aalen University, Aalen, Germany
Interests: neural networks; intelligent control systems; secure communication; image processing; switched control systems

Special Issue Information

Dear Colleagues,

Neural Network approaches have made significant advancements and have been effectively utilized in numerous domains such as signal processing, pattern recognition, system control, and mathematical modeling. Particularly, the use of neural networks in nonlinear system identification and control is largely motivated by their major benefits of highly parallel structure, nonlinear function approximation, fault tolerance, learning capability, and efficient analog VLSI implementation for real-time applications. Numerous nonlinearities, unmeasurable noise, unmodeled dynamics, multi-loop, etc., are the present challenges for engineers when implementing control techniques in many real-world systems. On the other hand, fractional calculus has received much attention among researchers due to its advantages of more degrees of freedom and significant properties. Recently, many researchers have been involved in the initiation of research on fractional-order control systems and their applications. However, very few works are analyzed for dynamical properties and applications in the field of control systems, fuzzy control, and signal processing. This Special Issue will serve as a useful guide on techniques for stability analysis, optimal control problems, secure control techniques, and power systems.

Some of the related subjects that deserve to be studied and deepened are as follows:

  • Study of dynamic analyzing the control systems;
  • Applications of control systems in science and engineering;
  • Fractional-order sliding mode control;
  • Neural network control;
  • Stochastic control systems;
  • Adaptive and optimal control;
  • Interconnected nonlinear systems;
  • Micro-grid control systems;
  • Multi-agent Systems;
  • Study of mathematical modeling of neural networks;
  • Image processing;
  • Applications of type-1 and type-2 fuzzy control systems;
  • Fault detection and fault tolerance control.

Prof. Dr. P. Balasubramaniam
Dr. R. Vijay Aravind
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • control systems
  • nonlinear systems
  • stability
  • synchronization analysis
  • fractional-order nonlinear systems
  • neural networks
  • mathematical modeling
  • fuzzy logics 

Published Papers (7 papers)

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Research

20 pages, 533 KiB  
Article
Fixed/Preassigned-Time Synchronization of Fully Quaternion-Valued Cohen–Grossberg Neural Networks with Generalized Time Delay
by Shichao Jia, Cheng Hu and Haijun Jiang
Mathematics 2023, 11(23), 4825; https://doi.org/10.3390/math11234825 - 29 Nov 2023
Viewed by 652
Abstract
This article is concerned with fixed-time synchronization and preassigned-time synchronization of Cohen–Grossberg quaternion-valued neural networks with discontinuous activation functions and generalized time-varying delays. Firstly, a dynamic model of Cohen–Grossberg neural networks is introduced in the quaternion field, where the time delay successfully integrates [...] Read more.
This article is concerned with fixed-time synchronization and preassigned-time synchronization of Cohen–Grossberg quaternion-valued neural networks with discontinuous activation functions and generalized time-varying delays. Firstly, a dynamic model of Cohen–Grossberg neural networks is introduced in the quaternion field, where the time delay successfully integrates discrete-time delay and proportional delay. Secondly, two types of discontinuous controllers employing the quaternion-valued signum function are designed. Without utilizing the conventional separation technique, by developing a direct analytical approach and using the theory of non-smooth analysis, several adequate criteria are derived to achieve fixed-time synchronization of Cohen–Grossberg neural networks and some more precise convergence times are estimated. To cater to practical requirements, preassigned-time synchronization is also addressed, which shows that the drive-slave networks reach synchronization within a specified time. Finally, two numerical simulations are presented to validate the effectiveness of the designed controllers and criteria. Full article
(This article belongs to the Special Issue Artificial Neural Networks and Dynamic Control Systems)
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42 pages, 17234 KiB  
Article
Metaheuristic Procedures for the Determination of a Bank of Switching Observers toward Soft Sensor Design with Application to an Alcoholic Fermentation Process
by Nikolaos D. Kouvakas, Fotis N. Koumboulis, Dimitrios G. Fragkoulis and George F. Fragulis
Mathematics 2023, 11(23), 4733; https://doi.org/10.3390/math11234733 - 22 Nov 2023
Viewed by 578
Abstract
The present work focused on the development of soft sensors for single-input single-output (SISO) nonlinear dynamic systems with unknown physical parameters using a switching observer design. Toward the development of more accurate soft sensors, as compared with hard sensors, an extended design methodology [...] Read more.
The present work focused on the development of soft sensors for single-input single-output (SISO) nonlinear dynamic systems with unknown physical parameters using a switching observer design. Toward the development of more accurate soft sensors, as compared with hard sensors, an extended design methodology for the determination of a bank of operating points satisfying the dense web principle was proposed, where for the determination of the bank of operating points and the observer parameters, a metaheuristic procedure was developed. To validate the results of the metaheuristic algorithm, the case of an alcoholic fermentation process was studied as a special case of the present approach. For the nonlinear model of the process, an observer-based soft sensor was developed using the metaheuristic procedure. First, the accuracy of the linear approximant of the process with respect to the original nonlinear model was investigated. Second, the I/O reconstructability of the linear approximant was verified. Third, based on the linear approximant, an observer was designed for the estimation of the non-measurable variable. Fourth, considering that the observer is designed upon the linear approximant, the linear approximant model parameters are derived through identification, for different operating points, upon the nonlinear model. Fifth, the observers corresponding to the different operating points, constitute a bank of observers. The design was completed using a data-driven rule-based system, performing stepwise switching between the observers of the bank. The efficiency of the proposed metaheuristic algorithm and the performance of the switching scheme were demonstrated through a series of computational experiments, where it was observed that the herein-proposed approach was more than two orders of magnitude more accurate than traditional single-step approaches of transition from one operating point to another. Full article
(This article belongs to the Special Issue Artificial Neural Networks and Dynamic Control Systems)
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15 pages, 1010 KiB  
Article
A Simplified Controller Design for Fixed/Preassigned-Time Synchronization of Stochastic Discontinuous Neural Networks
by Haoyu Li, Leimin Wang and Wenwen Shen
Mathematics 2023, 11(21), 4414; https://doi.org/10.3390/math11214414 - 25 Oct 2023
Viewed by 622
Abstract
This paper addresses the synchronization problem of delayed stochastic neural networks with discontinuous activation functions (DSNNsDF), specifically focusing on fixed/preassigned-time synchronization. The objective is to develop a class of simplified controllers capable of effectively addressing the challenges posed by time delays, discontinuous activation [...] Read more.
This paper addresses the synchronization problem of delayed stochastic neural networks with discontinuous activation functions (DSNNsDF), specifically focusing on fixed/preassigned-time synchronization. The objective is to develop a class of simplified controllers capable of effectively addressing the challenges posed by time delays, discontinuous activation functions, and stochastic perturbations during the synchronization process. In this regard, we propose several controllers with simpler structures to achieve the desired preassigned-time synchronization (PTS) result. To enhance the accuracy of time estimation, stochastic fixed-time control theory is employed. Rigorous numerical simulations are conducted to validate the effectiveness of our approach. The utilization of our proposed results significantly improves the performance of the synchronization controller for DSNNsDF, thereby enabling advancements and diverse applications in the field. Full article
(This article belongs to the Special Issue Artificial Neural Networks and Dynamic Control Systems)
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20 pages, 3259 KiB  
Article
Neuroadaptive Dynamic Surface Asymptotic Tracking Control of a VTOL Aircraft with Unknown Dynamics and External Disturbances
by Xianhao Yang, Xiongfeng Deng, Liang Tao and Binzi Xu
Mathematics 2023, 11(12), 2725; https://doi.org/10.3390/math11122725 - 15 Jun 2023
Viewed by 753
Abstract
This work studies the asymptotic tracking control problem of a vertical take-off and landing (VTOL) aircraft with unknown dynamics and external disturbances. The unknown nonlinear dynamics of the VTOL aircraft are approximated via the introduction of radial basis function neural networks. Then, the [...] Read more.
This work studies the asymptotic tracking control problem of a vertical take-off and landing (VTOL) aircraft with unknown dynamics and external disturbances. The unknown nonlinear dynamics of the VTOL aircraft are approximated via the introduction of radial basis function neural networks. Then, the weight update laws are designed. Furthermore, the parameter update control laws are presented to deal with the errors generated during the approximation process and the external disturbances of the aircraft system. Moreover, first-order filters are introduced to avoid repeated differentiation of the designed virtual control laws, thereby effectively eliminating the “complexity explosion” problem caused by traditional backstepping control. Based on the application of the neural network control method, dynamic surface control technique, weight update laws and parameter update control laws, neuroadaptive dynamic surface control laws for the aircraft system are finally proposed. Theoretical analysis shows that the proposed control law can ensure that the aircraft system asymptotically tracks the reference trajectories and the tracking errors can converge to a small neighborhood of zero by choosing the appropriate designed parameters. Finally, simulation examples are provided to verify the effectiveness of proposed control laws. Full article
(This article belongs to the Special Issue Artificial Neural Networks and Dynamic Control Systems)
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25 pages, 5156 KiB  
Article
Fixed-Time RBFNN-Based Prescribed Performance Control for Robot Manipulators: Achieving Global Convergence and Control Performance Improvement
by Anh Tuan Vo, Thanh Nguyen Truong and Hee-Jun Kang
Mathematics 2023, 11(10), 2307; https://doi.org/10.3390/math11102307 - 15 May 2023
Cited by 6 | Viewed by 1135
Abstract
This paper proposes a fixed-time neural network-based prescribed performance control method (FNN-PPCM) for robot manipulators. A fixed-time sliding mode controller (SMC) is designed with its strengths and weaknesses in mind. However, to address the limitations of the controller, the paper suggests alternative approaches [...] Read more.
This paper proposes a fixed-time neural network-based prescribed performance control method (FNN-PPCM) for robot manipulators. A fixed-time sliding mode controller (SMC) is designed with its strengths and weaknesses in mind. However, to address the limitations of the controller, the paper suggests alternative approaches for achieving the desired control objective. To maintain stability during a robot’s operation, it is crucial to keep error states within a set range. To form the unconstrained systems corresponding to the robot’s constrained systems, we apply modified prescribed performance functions (PPFs) and transformed errors set. PPFs help regulate steady-state errors within a performance range that has symmetric boundaries around zero, thereby ensuring that the tracking error is zero when the transformed error is zero. Additionally, we use a singularity-free sliding surface designed using transformed errors to determine the fixed-time convergence interval and maximum allowable control errors during steady-state operation. To address lumped uncertainties, we employ a radial basis function neural network (RBFNN) that approximates their value directly. By selecting the transformed errors as the input for the RBFNN, we can minimize these errors while bounding the tracking errors. This results in a more accurate and faster estimation, which is superior to using tracking errors as the input for the RBFNN. The design procedure of our approach is based on fixed-time SMC combined with PPC. The method integrates an RBFNN for precise uncertainty estimation, unconstrained dynamics, and a fixed-time convergence sliding surface based on the transformed error. By using this design, we can achieve fixed-time prescribed performance, effectively address chattering, and only require a partial dynamics model of the robot. We conducted numerical simulations on a 3-DOF robot manipulator to confirm the effectiveness and superiority of the FNN-PPCM. Full article
(This article belongs to the Special Issue Artificial Neural Networks and Dynamic Control Systems)
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17 pages, 934 KiB  
Article
Fixed/Preassigned-Time Stabilization for Complex-Valued Inertial Neural Networks with Distributed Delays: A Non-Separation Approach
by Yu Yao, Guodong Zhang and Yan Li
Mathematics 2023, 11(10), 2275; https://doi.org/10.3390/math11102275 - 12 May 2023
Cited by 3 | Viewed by 1109
Abstract
This article explores complex-valued inertial neural networks (CVINNs) with distributed delays (DDs). By constructing two new feedback controllers, some novel results on fixed-time stabilization (FTS) and preassigned-time stabilization (PTS) of CVINNs are established. Unlike most of the previous works, FTS and PTS obtained [...] Read more.
This article explores complex-valued inertial neural networks (CVINNs) with distributed delays (DDs). By constructing two new feedback controllers, some novel results on fixed-time stabilization (FTS) and preassigned-time stabilization (PTS) of CVINNs are established. Unlike most of the previous works, FTS and PTS obtained here are explored without dividing the original complex-valued system into two separate real valued subsystems. Eventually, to verify the effectiveness and reliability of the results of this article, we provide several numerical examples. The FTS and PTS of CVINNs are successfully implemented at T = 6, 5.5, and 5, and the settling time is not affected by system parameters and initial values. Full article
(This article belongs to the Special Issue Artificial Neural Networks and Dynamic Control Systems)
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21 pages, 3017 KiB  
Article
Gated Recurrent Fuzzy Neural Network Sliding Mode Control of a Micro Gyroscope
by Jiapeng Xie, Juntao Fei and Cuicui An
Mathematics 2023, 11(3), 509; https://doi.org/10.3390/math11030509 - 18 Jan 2023
Viewed by 916
Abstract
This paper proposes a non-singular fast terminal sliding mode control (NFTSMC) method for micro gyroscopes with unknown uncertainty based on gated recurrent fuzzy neural networks (GRFNNs). First, taking advantage of non-singular fast terminal sliding control, a sliding hyperplane is designed with a nonlinear [...] Read more.
This paper proposes a non-singular fast terminal sliding mode control (NFTSMC) method for micro gyroscopes with unknown uncertainty based on gated recurrent fuzzy neural networks (GRFNNs). First, taking advantage of non-singular fast terminal sliding control, a sliding hyperplane is designed with a nonlinear function to ensure that the tracking error of the system converges to zero within a specified finite time. Then, the unknown model parameters of the micro gyroscope are estimated using a GRFNN. Since the GRFNN can adaptively adjust the base width, center vector, gated recurrent unit parameters, and outer gains, it can achieve accurate approximation to unknown models, enhancing the robustness and accuracy. In addition, due to the introduction of gated recurrent units, The GRFNN can effectively utilize the previous data and avoid the problem of gradient disappearance. The comparison of the simulation results with traditional neural sliding mode control shows that the proposed method can achieve better tracking performance and more accurate estimation of unknown models. Full article
(This article belongs to the Special Issue Artificial Neural Networks and Dynamic Control Systems)
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