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Mathematics
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Control Problem of Nonlinear Systems with Applications, 2nd Edition
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Control Problem of Nonlinear Systems with Applications, 2nd Edition

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

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 3207

Special Issue Editors

Prof. Dr. Rongwei Guo

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
Interests: chaos control; chaos synchronization; switched systems; nonlinear systems
Special Issues, Collections and Topics in MDPI journals
Dr. Cuimei Jiang

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
Interests: chaos control; chaos synchronization; nonlinear systems
Special Issues, Collections and Topics in MDPI journals
Dr. Ruimin Xu

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
Interests: stochastic control; stochastic differential equation; nonlinear systems; game theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The control of nonlinear systems constitutes a general problem in actual processes and has attracted many scholars owing to its wide applications in various fields such as physics, mathematics, finance, transportation, and engineering. Therefore, the analysis and synthesis of the control problem play important roles in many practical systems.

The aim of this Special Issue is to bring together the latest/innovative knowledge and analysis and synthesis of the control problem of nonlinear systems. All submissions are expected to include original ideas and novel approaches. We invite authors to contribute original research articles related to all aspects of this Special Issue.

Prof. Dr. Rongwei Guo
Dr. Cuimei Jiang
Dr. Ruimin Xu
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

  • chaos control
  • chaos synchronization
  • nonlinear systems
  • switched systems
  • stochastic control
  • stochastic differential equation

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Published Papers (3 papers)

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Research

17 pages, 1305 KiB  
Article
Clustering Component Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control
by Jie Liu and Jian-Ping Sun
Mathematics 2024, 12(7), 1022; https://doi.org/10.3390/math12071022 - 28 Mar 2024
Viewed by 716
Abstract
In this paper, the problem of clustering component synchronization of nonlinearly coupled complex networks with nonidentical nodes and asymmetric couplings is investigated. A pinning control strategy is designed to achieve the clustering component synchronization with respect to the specified components. Based on matrix [...] Read more.
In this paper, the problem of clustering component synchronization of nonlinearly coupled complex networks with nonidentical nodes and asymmetric couplings is investigated. A pinning control strategy is designed to achieve the clustering component synchronization with respect to the specified components. Based on matrix analysis and stability theory, clustering component synchronization criteria are established. Two numerical simulations are also provided to show the effectiveness of the theoretical results. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications, 2nd Edition)
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10 pages, 2988 KiB  
Article
Optimal Control Strategy for SLBRS with Two Control Inputs
by Xiangqing Zhao
Mathematics 2023, 11(19), 4036; https://doi.org/10.3390/math11194036 - 22 Sep 2023
Cited by 3 | Viewed by 921
Abstract
Computer virus attacks result in significant losses each year, drawing considerable attention from enterprises, governments, academic institutions, and various other sectors. Researchers have proposed various approaches to fight against computer viruses, including antivirus software and internet firewalls. In this paper, we focus on [...] Read more.
Computer virus attacks result in significant losses each year, drawing considerable attention from enterprises, governments, academic institutions, and various other sectors. Researchers have proposed various approaches to fight against computer viruses, including antivirus software and internet firewalls. In this paper, we focus on investigating computer virus transmission from the perspective of mathematical modeling. Our main contributions in this paper are threefold: (1) we improve the classical SLBRS model by incorporating cure rates, effectively capturing the dynamics of computer network maintenance; (2) we introduce an optimal control system within the SLBRS framework, with the dual objectives of minimizing network detoxification costs and reducing the proportion of broken-out nodes; and (3) by employing Pontryagin’s Maximum Principle, we establish the existence and uniqueness of an optimal control strategy for the proposed control system. Furthermore, we perform numerical simulations to demonstrate the effectiveness of our theoretical analyses. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications, 2nd Edition)
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19 pages, 4290 KiB  
Article
Recurrent Neural Network with Finite Time Sampling for Dynamics Identification in Rehabilitation Robots
by Ahmed Alotaibi and Hajid Alsubaie
Mathematics 2023, 11(17), 3731; https://doi.org/10.3390/math11173731 - 30 Aug 2023
Cited by 1 | Viewed by 1087
Abstract
Rehabilitation robots can establish a direct connection between the user’s nerve signals and the robot’s actuators by integrating with the human nervous system. However, uncertainties in these systems limit their performance and accuracy. To address this challenge, the current study introduces an algorithm [...] Read more.
Rehabilitation robots can establish a direct connection between the user’s nerve signals and the robot’s actuators by integrating with the human nervous system. However, uncertainties in these systems limit their performance and accuracy. To address this challenge, the current study introduces an algorithm that effectively identifies and predicts unfamiliar dynamics in lower-limb rehabilitation robots. To accomplish this, the current study initially presents the dynamic model of a knee rehabilitation robot. Then, a finite time sampler is developed and the algorithm is proposed. In the proposed algorithm, the electromyographic signals are input into the rehabilitation robot. Via the use of a guaranteed stable sampler, samples from the unknown dynamics are extracted. By training the recurrent neural network with the acquired samples, the algorithm effectively learns and captures the underlying patterns of the unknown dynamics. The proposed recurrent neural network is enhanced with a self-attention mechanism, which plays a vital role in devising effective strategies for practical applications. Numerical simulation demonstrates the algorithm’s effectiveness, highlighting its excellent performance in identifying the system’s unknown dynamics. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications, 2nd Edition)
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