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Mathematics
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Advanced Control of Complex Dynamical Systems with Applications
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Advanced Control of Complex Dynamical Systems with Applications

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

Deadline for manuscript submissions: 10 September 2025 | Viewed by 7965

Special Issue Editors

Dr. Belem Saldivar

E-Mail Website
Guest Editor
Department of Automatic Control, CINVESTAV-IPN, Av. Instituto Politécnico Nacional 2508, Mexico City 07360, Mexico
Interests: nonlinear control; time-delay systems; biomedical systems; renewable energy systems; mechanical vibration control
Dr. Lizeth Torres Ortíz

E-Mail Website
Guest Editor
Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad de México 04510, Mexico
Interests: hydro-informatics; fault diagnosis; fluid systems

Special Issue Information

Dear Colleagues,

Complex dynamical systems, which consist of multiple subsystems with intricate interactions, are pervasive across various fields such as engineering, chemistry, biology, and physics. Studying the control and analysis of complex systems has become increasingly important due to several factors. Firstly, it allows us to understand emergent behavior, where collective patterns arise from individual interactions. Secondly, it helps optimize system efficiency in fields like engineering. Additionally, it aids in managing and mitigating the challenges associated with system complexity. Furthermore, it enables us to predict and prevent system failures and design resilient systems capable of adapting and maintaining functionality. Overall, the study of complex systems offers insights and strategies with broad implications across diverse domains, leading to advancements in technology, science, and decision-making processes.

With this in mind, we are pleased to announce a Special Issue that aims to explore and showcase cutting-edge developments in the analysis and control of complex dynamical systems and their practical applications. We are particularly interested in articles that enhance our understanding of the observed phenomena in these systems through comprehensive analytic advancements, numerical simulations, and experimental testing.

We invite high-quality contributions encompassing original research results as well as survey articles in the following fields:

  • Hybrid systems;
  • Multi-agent systems;
  • Diagnosis and prognosis of complex systems;
  • Nonlinear dynamics and chaos;
  • Time-delay systems;
  • Autonomous, non-autonomous, and piecewise-smooth dynamical systems;
  • Passivity-based control;
  • Adaptive control;
  • Robust control;
  • Neural networks.

By bringing together diverse perspectives and insights, this Special Issue aims to foster collaboration and contribute to the collective knowledge in the analysis and control of complex dynamical systems. We look forward to your valuable contributions and the advancement of this exciting field.

Best regards,

Dr. Belem Saldivar
Dr. Lizeth Torres Ortíz
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 theory
  • complex dynamical systems
  • stability and stabilization
  • practical applications

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Published Papers (6 papers)

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Research

23 pages, 826 KiB  
Article
Verification of Opacity Under a K-Delay Orwellian Observation Mechanism
by Jiahui Zhang, Kuize Zhang, Xiaoguang Han and Zhiwu Li
Mathematics 2025, 13(10), 1568; https://doi.org/10.3390/math13101568 - 9 May 2025
Viewed by 149
Abstract
Opacity, an important property of the information flow in discrete-event systems (DESs), characterizes whether the secret information in a system is ambiguous to a passive observer (called an intruder). Observation models play a critical role in the analysis of opacity. In this paper, [...] Read more.
Opacity, an important property of the information flow in discrete-event systems (DESs), characterizes whether the secret information in a system is ambiguous to a passive observer (called an intruder). Observation models play a critical role in the analysis of opacity. In this paper, instead of adopting a fully static observation model or a fully dynamic observation model, we use a novel Orwellian-type observation model to study the verification of the current-state opacity (CSO), where the observability of an unobservable event can be re-interpreted once certain/several specific conditions are met. First, a K-delay Orwellian observation mechanism (KOOM) is proposed as a novel Orwellian-type observation mechanism for extending the existing Orwellian projection. The main characteristics of the KOOM are delaying the inevitable information release and narrowing the release range for historical information to protect the secrets in a system to a greater extent than with the existing Orwellian projection. Second, we formulate the definitions of standard and strong CSO under the KOOM. Finally, we address the verification problem for these two types of opacity by constructing two novel information structures called a standard K-delay verifier and a strong K-delay verifier, respectively. An analysis of the computational complexity and illustrative examples are also presented for the proposed results. Overall, the proposed notions of standard and strong CSO under the KOOM capture the security privacy requirements regarding a delayed release in applications, such as intelligent transportation systems, etc. Full article
(This article belongs to the Special Issue Advanced Control of Complex Dynamical Systems with Applications)
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21 pages, 5677 KiB  
Article
Large Language Model and Digital Twins Empowered Asynchronous Federated Learning for Secure Data Sharing in Intelligent Labeling
by Xuanzhu Sheng, Chao Yu, Xiaolong Cui and Yang Zhou
Mathematics 2024, 12(22), 3550; https://doi.org/10.3390/math12223550 - 13 Nov 2024
Viewed by 2054
Abstract
With the advancement of the large language model (LLM), the demand for data labeling services has increased dramatically. Big models are inseparable from high-quality, specialized scene data, from training to deploying application iterations to landing generation. However, how to achieve intelligent labeling consistency [...] Read more.
With the advancement of the large language model (LLM), the demand for data labeling services has increased dramatically. Big models are inseparable from high-quality, specialized scene data, from training to deploying application iterations to landing generation. However, how to achieve intelligent labeling consistency and accuracy and improve labeling efficiency in distributed data middleware scenarios is the main difficulty in enhancing the quality of labeled data at present. In this paper, we proposed an asynchronous federated learning optimization method based on the combination of LLM and digital twin technology. By analysising and comparing and with other existing asynchronous federated learning algorithms, the experimental results show that our proposed method outperforms other algorithms in terms of performance, such as model accuracy and running time. The experimental validation results show that our proposed method has good performance compared with other algorithms in the process of intelligent labeling both in terms of accuracy and running solves the consistency and accuracy problems of intelligent labeling in a distributed data center. Full article
(This article belongs to the Special Issue Advanced Control of Complex Dynamical Systems with Applications)
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24 pages, 3921 KiB  
Article
Graph Neural Network Based Asynchronous Federated Learning for Digital Twin-Driven Distributed Multi-Agent Dynamical Systems
by Xuanzhu Sheng, Yang Zhou and Xiaolong Cui
Mathematics 2024, 12(16), 2469; https://doi.org/10.3390/math12162469 - 9 Aug 2024
Cited by 1 | Viewed by 1533
Abstract
The rapid development of artificial intelligence (AI) and 5G paradigm brings infinite possibilities for data annotation for new applications in the industrial Internet of Things (IIoT). However, the problem of data annotation consistency under distributed architectures and growing concerns about issues such as [...] Read more.
The rapid development of artificial intelligence (AI) and 5G paradigm brings infinite possibilities for data annotation for new applications in the industrial Internet of Things (IIoT). However, the problem of data annotation consistency under distributed architectures and growing concerns about issues such as data privacy and cybersecurity are major obstacles to improving the quality of distributed data annotation. In this paper, we propose a reputation-based asynchronous federated learning approach for digital twins. First, this paper integrates digital twins into an asynchronous federated learning framework, and utilizes a smart contract-based reputation mechanism to enhance the interconnection and internal interaction of asynchronous mobile terminals. In addition, in order to enhance security and privacy protection in the distributed smart annotation system, this paper introduces blockchain technology to optimize the data exchange, storage, and sharing process to improve system security and reliability. The data results show that the consistency of our proposed FedDTrep distributed intelligent labeling system reaches 99%. Full article
(This article belongs to the Special Issue Advanced Control of Complex Dynamical Systems with Applications)
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19 pages, 5503 KiB  
Article
Modeling and Control of the High-Voltage Terminal of a Tandem Van de Graaff Accelerator
by Efrén Gutiérrez Ocampo, Belem Saldivar, Juan Carlos Ávila Vilchis and Otniel Portillo-Rodríguez
Mathematics 2024, 12(15), 2335; https://doi.org/10.3390/math12152335 - 26 Jul 2024
Viewed by 1296
Abstract
This paper presents a mathematical model derived from an equivalent electrical circuit to describe the dynamic behavior of the high-voltage terminal of a tandem Van de Graaff accelerator. Two approaches are presented for modeling the transit time of the current flowing through the [...] Read more.
This paper presents a mathematical model derived from an equivalent electrical circuit to describe the dynamic behavior of the high-voltage terminal of a tandem Van de Graaff accelerator. Two approaches are presented for modeling the transit time of the current flowing through the corona needles. The first one considers an equivalent self-inductance in the corona triode, whereas, in the second one, the transit time is represented by a delay in the corona current. The validation of the proposed models was carried out through experimental tests developed at the National Nuclear Research Institute of Mexico. Furthermore, two strategies for controlling the slow variations of the terminal voltage limited by the slow response of the control loop based on corona discharge are evaluated: a Proportional–Integral–Derivative controller and a sliding mode controller. The Root-Mean-Squared Error calculation leads to the conclusion that both control strategies are suitable for regulating the voltage at the accelerator potential terminal. However, the sliding mode controller leads to an overshoot-free response and a shorter settling time. Full article
(This article belongs to the Special Issue Advanced Control of Complex Dynamical Systems with Applications)
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17 pages, 1200 KiB  
Article
Trajectory Tracking Control of an Autonomous Vessel in the Presence of Unknown Dynamics and Disturbances
by Carlos Aguilar-Ibanez, Miguel S. Suarez-Castanon, Eloísa García-Canseco, Jose de Jesus Rubio, Ricardo Barron-Fernandez and Juan Carlos Martinez
Mathematics 2024, 12(14), 2239; https://doi.org/10.3390/math12142239 - 18 Jul 2024
Cited by 3 | Viewed by 903
Abstract
We present a proportional–integral–derivative-based controller plus an adaptive slide surface to solve the trajectory tracking control problem for a fully actuated vessel with unknown parameters perturbed by slowly varying external unknown dynamics. The controller design assumes that the vessel moves at low speed [...] Read more.
We present a proportional–integral–derivative-based controller plus an adaptive slide surface to solve the trajectory tracking control problem for a fully actuated vessel with unknown parameters perturbed by slowly varying external unknown dynamics. The controller design assumes that the vessel moves at low speed and frequency, its physical parameters are unknown, and its state is measurable. The control approach ensures error tracking convergence toward a small vicinity at the origin. We conduct the corresponding stability analysis using the Lyapunov theory and saturation functions. We tested the controller through two numerical experiments—a turning ellipse maneuver and a rest-to-rest maneuver—where the vessel parameters were unknown, and we obtained satisfactory results. Full article
(This article belongs to the Special Issue Advanced Control of Complex Dynamical Systems with Applications)
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25 pages, 2616 KiB  
Article
Sliding Surface-Based Path Planning for Unmanned Aerial Vehicle Aerobatics
by Oleg Cravioto, Belem Saldivar, Manuel Jiménez-Lizárraga, Juan Carlos Ávila-Vilchis and Carlos Aguilar-Ibañez
Mathematics 2024, 12(7), 1047; https://doi.org/10.3390/math12071047 - 30 Mar 2024
Viewed by 1127
Abstract
This paper exploits the concept of nonlinear sliding surfaces to be used as a basis in the development of aerial path planning projects involving aerobatic three-dimensional path curves in the presence of disturbances. This approach can be used for any kind of unmanned [...] Read more.
This paper exploits the concept of nonlinear sliding surfaces to be used as a basis in the development of aerial path planning projects involving aerobatic three-dimensional path curves in the presence of disturbances. This approach can be used for any kind of unmanned aerial vehicle aimed at performing aerobatic maneuvers. Each maneuver is associated with a nonlinear surface on which an aerial vehicle could be driven to slide. The surface design exploits the properties of Viviani’s curve and the Hopf bifurcation. A vector form of the super twisting algorithm steers the vehicle to the prescribed surfaces. A suitable switching control law is proposed to shift between surfaces at different time instants. A practical stability analysis that involves the descriptor approach allows for determining the controller gains. Numerical simulations are developed to illustrate the accomplishment of the suggested aerobatic flight. Full article
(This article belongs to the Special Issue Advanced Control of Complex Dynamical Systems with Applications)
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