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Mathematics
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Advances in Complex Systems and Their Control Principles
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Advances in Complex Systems and Their Control Principles

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

Deadline for manuscript submissions: 31 August 2024 | Viewed by 2634

Special Issue Editors

Dr. Lotfi Beji

E-Mail Website
Guest Editor
IBISC Laboratory, University of Evry/Paris Saclay, 40 Rue du Pelvoux, 91020 Evry, France
Interests: control of vehicles and blimps modeling; identification and control of autonomous robots
Dr. Dalil Ichalal

E-Mail Website
Guest Editor
Laboratoire Informatique, Biologie Intégrative et Systèmes Complexes, Université d'Evry Val d'Essonne, 91020 Evry, France
Interests: nonlinear state estimation and observer/controller design; set invariance; Takagi-Sugeno fuzzy modeling; time-delay and sampled data systems; fault diagnosis and fault tolerant control of nonlinear systems; application on vehicles and motorcycles dynamics

Special Issue Information

Dear Colleagues,

The evolution of the industrial world and the needs of contemporary consumer society has led to increased attention being given to physical and biological system dynamics. For example, system–system and human–system interactions introduce complexity and ingenuity in the dynamic modeling of interactions and control design. Subject to some constraints, our transportation modes and our security requirements are evolving. Our way of communication is also evolving, and even the satisfaction of our well-being is impacted by the evolution of the environment and its complexity. Hence, advances in complex systems and their control principles, as an open research domain, can help us to answer further societal needs and future industrial orientations in terms of transportation, communication and health. In interaction with static or dynamic environments, these advances require the construction of relevant mathematical models and control algorithms with more elaborated measurement prediction for system states that integrate data fusion and optimization.

The main objectives of this Special Issue will focus on the dynamic behavior and stability of complex systems based on finite and infinite dimensional dynamics and their interaction. Known or unknown dynamic environments that affect complex system stability and transition are within the scope.

We invite authors to contribute research articles addressing significant issues and contributing to control principles with advancements in complex systems and their interaction. We welcome contributions in all domains that permit the emphasis of mathematical and numerical aspects while control principles are required. 

Dr. Lotfi Beji
Dr. Dalil Ichalal
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

  • finite and infinite dimensional dynamics
  • dynamical systems and environment
  • large-scale systems
  • control principles
  • systems in interaction for health
  • systems in interaction for production
  • systems in interaction for rescue

Published Papers (2 papers)

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Research

22 pages, 3466 KiB  
Article
Position and Attitude Tracking Finite-Time Adaptive Control for a VTOL Aircraft Using Global Fast Terminal Sliding Mode Control
by Xiongfeng Deng, Yiqing Huang, Binzi Xu and Liang Tao
Mathematics 2023, 11(12), 2732; https://doi.org/10.3390/math11122732 - 16 Jun 2023
Viewed by 1068
Abstract
In this work, the position and attitude tracking finite-time adaptive control problem of a type of vertical take-off and landing (VTOL) aircraft system is studied. Here, the dynamic of the VTOL aircraft is subjected to external disturbances and unknown nonlinearities. Firstly, radial basis [...] Read more.
In this work, the position and attitude tracking finite-time adaptive control problem of a type of vertical take-off and landing (VTOL) aircraft system is studied. Here, the dynamic of the VTOL aircraft is subjected to external disturbances and unknown nonlinearities. Firstly, radial basis function neural networks are introduced to approximate these unknown nonlinearities, and adaptive weight update laws are proposed to replace unknown ideal weights. Secondly, for the errors generated in the approximation process and the external disturbances of the aircraft system, adaptive parameter update laws are presented. After that, based on the designed global fast terminal sliding mode control functions and adaptive update laws, we present the position tracking control laws and the roll angle control law. Then, based on this, the adaptive global fast terminal sliding control laws for the given aircraft system are finally obtained. Meanwhile, the stability of the aircraft control system is proven by using Lyapunov stability theory and designed adaptive control laws. It is not only ensured that the outputs of the aircraft system can track the given trajectories, but also ensured that the tracking errors can converge to approximately zero within a finite time. Finally, the validity of the designed adaptive control laws is verified through three numerical examples. It can be obtained that the finite-time tracking problems of the given aircraft system can be achieved at 18.8766 s and 14.6340 s under the given parameters. The results are consistent with the theoretical analysis. In addition, under the control laws proposed in this work, the aircraft system can achieve tracking after 9.443 s and 9.674 s and the tracking errors are basically close to zero, which is significantly superior to other control methods considered in this work. Full article
(This article belongs to the Special Issue Advances in Complex Systems and Their Control Principles)
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13 pages, 532 KiB  
Article
Spectral Analysis of the Infinite-Dimensional Sonic Drillstring Dynamics
by Kaïs Ammari and Lotfi Beji
Mathematics 2023, 11(11), 2426; https://doi.org/10.3390/math11112426 - 24 May 2023
Viewed by 888
Abstract
By deploying sonic drilling for soil structure fracturing in the presence of consolidated/ unconsolidated formations, this technique greatly reduces the friction on the drillstring and bit by using energetic resonance, a bit-bouncing high-frequency axial vibration. While resonance must be avoided, to our knowledge, [...] Read more.
By deploying sonic drilling for soil structure fracturing in the presence of consolidated/ unconsolidated formations, this technique greatly reduces the friction on the drillstring and bit by using energetic resonance, a bit-bouncing high-frequency axial vibration. While resonance must be avoided, to our knowledge, drilling is the only application area where resonance is necessary to break up the rocks. The problem is that the machine’s tool can encounter several different geological layers with many varieties of density. Hence, keeping the resonance of the tool plays an important role in drill processes, especially in tunnel or infrastructure shoring. In this paper, we analyze the sonic drillstring dynamics as an infinite-dimensional system from another viewpoint using the frequency domain approach. From the operator theory in defining the adequate function spaces, we show the system well-posedness. The hydraulic produced axial force that should preserve the resonant drillstring mode is defined from the spectrum study of the constructed linear operator guided by the ratio control from the top to tip boundary magnitudes. Full article
(This article belongs to the Special Issue Advances in Complex Systems and Their Control Principles)
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