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Mathematics
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Advancements in Nonlinear Control Strategies
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Advancements in Nonlinear Control Strategies

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 30 June 2025 | Viewed by 1809

Special Issue Editor

Dr. Anh Tuan Vo

E-Mail Website
Guest Editor
Department of Electrical, Electronic and Computer Engineering, University of Ulsan, Ulsan 44610, Republic of Korea
Interests: sliding mode control, adaptive control, time-delay control, and prescribed performance control; intelligent control methods; fault diagnosis and fault-tolerant control; control of UAVs and AUVs

Special Issue Information

Dear Colleagues,

The Special Issue on "Advancements in Nonlinear Control Strategies" emphasizes the critical role of nonlinear control techniques in addressing the complexities of dynamic systems. Traditional linear methods often fall short in managing nonlinear phenomena, necessitating the development of innovative control methodologies.

We invite contributions in the following areas:

  • Advanced Control Strategies: Novel approaches to enhance the control of nonlinear systems;
  • Stability Analysis: Techniques for assessing and ensuring system stability;
  • Performance Optimization: Methods to improve the efficiency and effectiveness of control strategies;
  • Practical Applications: Implementations in robotics, unmanned aerial vehicles (UAVs), autonomous underwater vehicles (AUVs), and other nonlinear systems;
  • Intelligent Control Techniques: Integration of neural networks, fuzzy logic systems, model predictive control, reinforcement learning, and other techniques to bolster nonlinear control methodologies;
  • Simulation Results: Studies showcasing simulation outcomes that validate new control approaches.

This Special Issue aims to inspire new solutions and further research in the field of nonlinear control, providing a platform for sharing cutting-edge advancements and practical implementations.

Dr. Anh Tuan Vo
Guest Editor

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

  • nonlinear analysis
  • control theory
  • system dynamics
  • stability analysis
  • dynamic stability
  • nonlinear control
  • robust control
  • applications in engineering
  • intelligent control techniques
  • mathematical modeling
  • complex systems
  • uncertainties and disturbances

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

26 pages, 7333 KiB  
Article
Takagi–Sugeno–Kang Fuzzy Neural Network for Nonlinear Chaotic Systems and Its Utilization in Secure Medical Image Encryption
by Duc Hung Pham and Mai The Vu
Mathematics 2025, 13(6), 923; https://doi.org/10.3390/math13060923 - 11 Mar 2025
Viewed by 550
Abstract
This study introduces a novel control framework based on the Takagi–Sugeno–Kang wavelet fuzzy neural network, integrating brain imitated network and cerebellar network. The proposed controller demonstrates high robustness, making it an excellent candidate for handling intricate nonlinear dynamics, effectively mapping input–output relationships and [...] Read more.
This study introduces a novel control framework based on the Takagi–Sugeno–Kang wavelet fuzzy neural network, integrating brain imitated network and cerebellar network. The proposed controller demonstrates high robustness, making it an excellent candidate for handling intricate nonlinear dynamics, effectively mapping input–output relationships and efficiently learning from data. To enhance its performance, the controller’s parameters are fine-tuned using Lyapunov stability theory. Compared to existing approaches, the proposed model exhibits superior learning capabilities and achieves outstanding performance metrics. Furthermore, the study applies this synchronization technique to the secure transmission of medical images. By encrypting a medical image into a chaotic trajectory before transmission, the system ensures data security. On the receiving end, the original image is successfully reconstructed using chaotic trajectory synchronization. Experimental results confirm the effectiveness and reliability of the proposed neural network model, as well as the encryption and decryption process. Specifically, the average_RMSE of the Takagi–Sugeno–Kang fuzzy wavelet brain cerebral controller (TFWBCC) method is 2.004 times smaller than the cerebellar model articulation controller (CMAC) method, 1.923 times smaller than the RCMAC method, 1.8829 times smaller than the TSKCMAC method, and 1.8153 times smaller than the brain emotional learning controller (BELC) method. Full article
(This article belongs to the Special Issue Advancements in Nonlinear Control Strategies)
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25 pages, 7487 KiB  
Article
A Novel Time Delay Nonsingular Fast Terminal Sliding Mode Control for Robot Manipulators with Input Saturation
by Thanh Nguyen Truong, Anh Tuan Vo and Hee-Jun Kang
Mathematics 2025, 13(1), 119; https://doi.org/10.3390/math13010119 - 31 Dec 2024
Cited by 2 | Viewed by 970
Abstract
Manipulator systems are increasingly deployed across various industries to perform complex, repetitive, and hazardous tasks, necessitating high-precision control for optimal performance. However, the design of effective control algorithms is challenged by nonlinearities, uncertain dynamics, disturbances, and varying real-world conditions. To address these issues, [...] Read more.
Manipulator systems are increasingly deployed across various industries to perform complex, repetitive, and hazardous tasks, necessitating high-precision control for optimal performance. However, the design of effective control algorithms is challenged by nonlinearities, uncertain dynamics, disturbances, and varying real-world conditions. To address these issues, this paper proposes an advanced orbit-tracking control approach for manipulators, leveraging advancements in Time-Delay Estimation (TDE) and Fixed-Time Sliding Mode Control techniques. The TDE approximates the robot’s unknown dynamics and uncertainties, while a novel nonsingular fast terminal sliding mode (NFTSM) surface and novel fixed-time reaching control law (FTRCL) are introduced to ensure faster convergence within a fixed time and improved accuracy without a singularity issue. Additionally, an innovative auxiliary system is designed to address input saturation effects, ensuring that system states converge to zero within a fixed time even when saturation occurs. The Lyapunov-based theory is employed to prove the fixed-time convergence of the overall system. The effectiveness of the proposed controller is validated through simulations on a 3-DOF SAMSUNG FARA AT2 robot manipulator. Comparative analyses against NTSMC, NFTSMC, and GNTSMC methods demonstrate superior performance, characterized by faster convergence, reduced chattering, higher tracking accuracy, and a model-free design. These results underscore the potential of the proposed control strategy to significantly enhance the robustness, precision, and applicability of robotic systems in industrial environments. Full article
(This article belongs to the Special Issue Advancements in Nonlinear Control Strategies)
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