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Mathematics
Special Issues
Nonlinear Dynamics and Control: Challenges and Innovations
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Nonlinear Dynamics and Control: Challenges and Innovations

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 1 July 2025 | Viewed by 572

Special Issue Editor

Dr. Ning Cai

E-Mail Website
Guest Editor
Department of Artificial Intelligence, Beijing University of Posts and Telecommunications, Beijing 100876, China
Interests: complex dynamical system; robust control of nonlinear systems

Special Issue Information

Dear Colleagues,

Nonlinear dynamics and control are fundamental aspects of scientific inquiry and have far-reaching implications across a wide range of disciplines. From engineering and physics to biology and social sciences, nonlinear systems pervade our understanding of the world around us. This Special Issue will provide an invaluable platform to delve into the challenges faced in comprehending, analyzing, and controlling nonlinear systems, while also presenting novel approaches and innovative techniques that push the boundaries of current knowledge.

We seek high-quality contributions that illuminate the multifaceted aspects of nonlinear dynamics and control. Authors are encouraged to explore topics such as nonlinear control theory and applications, the application of chaos theory in control systems, nonlinear dynamics and stability analysis, bifurcation analysis and control, complex networks and their control, nonlinear time series analysis and prediction, dynamical systems and their control in engineering and physics, nonlinear control in biological and ecological systems, the role of nonlinear dynamics in social sciences and economics, as well as the use of nonlinear control in robotics and automation.

Dr. Ning Cai
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

  • complex dynamical system
  • nonlinear Dynamics
  • control theory
  • nonlinear systems

Published Papers (2 papers)

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Research

14 pages, 287 KiB  
Article
Fractional Neutral Integro-Differential Equations with Nonlocal Initial Conditions
by Zhiyuan Yuan, Luyao Wang, Wenchang He, Ning Cai and Jia Mu
Mathematics 2024, 12(12), 1877; https://doi.org/10.3390/math12121877 (registering DOI) - 16 Jun 2024
Viewed by 94
Abstract
We primarily investigate the existence of solutions for fractional neutral integro-differential equations with nonlocal initial conditions, which are crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, [...] Read more.
We primarily investigate the existence of solutions for fractional neutral integro-differential equations with nonlocal initial conditions, which are crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by using fixed-point theorems, we establish the existence of mild solutions under more relaxed conditions. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Control: Challenges and Innovations)
20 pages, 1208 KiB  
Article
Event-Triggered Adaptive Neural Prescribed Performance Tracking Control for Nonlinear Cyber–Physical Systems against Deception Attacks
by Chunyan Li, Yinguang Li, Jianhua Zhang and Yang Li
Mathematics 2024, 12(12), 1838; https://doi.org/10.3390/math12121838 - 13 Jun 2024
Viewed by 239
Abstract
This paper investigates the problem of the adaptive neural network tracking control of nonlinear cyber–physical systems (CPSs) subject to unknown deception attacks with prescribed performance. The considered system is under the influence of unknown deception attacks on both actuator and sensor networks, making [...] Read more.
This paper investigates the problem of the adaptive neural network tracking control of nonlinear cyber–physical systems (CPSs) subject to unknown deception attacks with prescribed performance. The considered system is under the influence of unknown deception attacks on both actuator and sensor networks, making the research problem challenging. The outstanding contribution of this paper is that a new anti-deception attack-prescribed performance tracking control scheme is proposed through a special coordinate transformation and funnel function, combined with backstepping and bounded estimation methods. The transient performance of the system can be ensured by the prescribed performance control scheme, which makes the indicators of the controlled system, such as settling time and tracking accuracy, able to be pre-assigned offline according to the task needs, and the applicability of the prescribed performance is tested by selecting different values of the settling time (0.5 s, 1 s, 1.5 s, 2 s, 2.5 s, and 3 s). In addition, to save the computational and communication resources of the CPS, this paper uses a finite-time differentiator to approximate the virtual control law differentiation to avoid “complexity explosion” and a switching threshold event triggering mechanism to save the communication resources for data transmission. Finally, the effectiveness of the proposed control strategy is further verified by an electromechanical system simulation example. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Control: Challenges and Innovations)
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