Modeling, Stability, and Control of Dynamic Systems and Their Applications

Topic Information

Dear Colleagues,

We are pleased to invite you to contribute to a Topic on "Modeling, Stability, and Control of Dynamic Systems and Their Applications". Dynamic systems are the backbone of modern advanced technology and science, with applications in various fields such as engineering, physics, biology, and economics. The study of dynamic systems involves three key components: modeling, stability analysis, and control design. In recent years, there have been significant advances in our understanding of dynamic systems and their applications, driven by the development of new theoretical frameworks, computational techniques, and experimental methods. This Topic aims to highlight recent advancements in these areas and their applications, showcasing the interdisciplinary nature of dynamic systems research. This Topic will include but is not limited to the following topics:

• Modeling analysis of dynamic systems in engineering;
• Robust/adaptive control and optimization techniques;
• Intermittent and sample-based control methodologies;
• Anti-disturbance control for dynamic systems with multi-disturbances;
• Guaranteed cost control and performance analysis for dynamic systems;
• Stochastic stability and stabilization;
• Hybrid systems, switched systems and delayed systems;
• Fractional control theory and fractional boundary value problems;
• Fractional dynamics and its applications in engineering and science;
• Numerical simulation and numerical algorithm;
• Applications of dynamic systems in biomathematics, economy and financial engineering.

We invite researchers to submit their original research papers, comprehensive review papers, and insightful perspectives that contribute to the advancement of knowledge in modeling, stability, and control of dynamic systems. The objective of this Topic is to provide a platform for researchers to disseminate their findings, engage in discussions about contemporary challenges, and explore new avenues in the study of dynamic systems and their applications.

Prof. Dr. Quanxin Zhu
Dr. Alexander Zaslavski
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
AppliedMath appliedmath	-	-	2021	25.3 Days	CHF 1000	Submit
Axioms axioms	1.9	-	2012	22.8 Days	CHF 2400	Submit
Fractal and Fractional fractalfract	3.6	4.6	2017	23.7 Days	CHF 2700	Submit
Mathematics mathematics	2.3	4.0	2013	18.3 Days	CHF 2600	Submit
Symmetry symmetry	2.2	5.4	2009	17.3 Days	CHF 2400	Submit

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Published Papers (7 papers)

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All AppliedMath Axioms Fractal Fract Mathematics Symmetry

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24 pages, 16861 KiB  

Open AccessArticle

Modeling a Multi-Lane Highway System Considering the Combined Impacts of Overtaking Mechanisms and Aggressive Lane-Changing Behaviors

by Shuhong Yang, Bin Huang, Chuan Tian and Yirong Kang

Mathematics 2025, 13(8), 1291; https://doi.org/10.3390/math13081291 - 15 Apr 2025

Viewed by 169

Abstract

This paper suggests a new multi-lane lattice model that incorporates both overtaking mechanisms and drivers’ aggressive lane-changing behaviors to investigate macroscopic traffic stability in multi-lane expressway environments. To enhance the fidelity of lane-changing simulation, the proposed model reformulates lane-changing protocols by integrating empirical [...] Read more.

This paper suggests a new multi-lane lattice model that incorporates both overtaking mechanisms and drivers’ aggressive lane-changing behaviors to investigate macroscopic traffic stability in multi-lane expressway environments. To enhance the fidelity of lane-changing simulation, the proposed model reformulates lane-changing protocols by integrating empirical observations of aggressive driving patterns in real-world scenarios. Through theoretical derivation, we formulate a density wave partial differential equation that captures the spatio-temporal propagation of congestion patterns near critical stability thresholds while analytically obtaining the linear stability criterion for the proposed model. The validity of these theoretical constructs is validated through systematic numerical simulation. Key findings reveal that when overtaking passing rates are relatively low, the driver’s aggressive lane-changing strategy exhibits a pronounced stabilizing effect on multi-lane systems and effectively mitigates traffic oscillation amplitudes. Conversely, under high passing rate conditions, such aggressive driving behaviors are shown to exert detrimental effects on both traffic fluctuation suppression and system-wide stability. Notably, our findings also demonstrate that expanding the number of lanes merges as a viable strategy to enhance systemic robustness. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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11 pages, 1301 KiB  

Open AccessArticle

Analyzing the Transient Process and the Realizability of Fractional Systems via Intermittent Control

by Jianbing Hu, Chuteng Ying, Shuguang Li, Zhe Jin, Xiaochao Chao and Xia Wang

Fractal Fract. 2025, 9(3), 184; https://doi.org/10.3390/fractalfract9030184 - 16 Mar 2025

Viewed by 175

Abstract

In this paper, we have studied the transient process and the realizability of fractional systems via intermittent control. For any system under intermittent control input, a transient oscillation process is inevitable when the input switches, which is irrelevant to mathematical model. But this [...] Read more.

In this paper, we have studied the transient process and the realizability of fractional systems via intermittent control. For any system under intermittent control input, a transient oscillation process is inevitable when the input switches, which is irrelevant to mathematical model. But this process is usually neglected when considering the achievements of fractional intermittent control systems as the initial value is changed by the switching input. The obtained theoretical results cannot agree with the real physical model. The input signal is treated as a piecewise signal by means of convolution operation and unit step function, and the output is drawn by convoluting the control input with a time decay function. We have drawn the conclusions that the initial value of the fractional model can not be updated by any outer input and that a transient process must exist that is related to all historic process and the memory property of a fractional system. If the response function of a system is taken as the time decay function, the results obtained are in good agreement with the actual model and can be used to analyze the transient phenomena in nature. Some examples are presented to verify our theoretical achievements. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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15 pages, 435 KiB  

Open AccessArticle

Verification of Detectability for Time Labeled Petri Net Systems with Unobservable Transitions

by Tao Qin and Zhiwu Li

Mathematics 2025, 13(4), 563; https://doi.org/10.3390/math13040563 - 8 Feb 2025

Viewed by 396

Abstract

We investigate the detectability verification problem of time-dependent systems modeled by time labeled Petri nets that are a typical time-dependent model of many computer-integrated systems in modern society, characterized by networked connections. In a time labeled Petri net, the detectability proposed in this [...] Read more.

We investigate the detectability verification problem of time-dependent systems modeled by time labeled Petri nets that are a typical time-dependent model of many computer-integrated systems in modern society, characterized by networked connections. In a time labeled Petri net, the detectability proposed in this paper characterizes the current state of a time-dependent system that can be uniquely determined after a finite number of observations within a given time instant. Moreover, we further define strong and weak detectability in a time labeled Petri net system. To verify strong and weak detectability, we excogitate a label-based state class graph, which is not required to enumerate all states of a system, to compute the states for a given real-time observation. Based on the proposed label-based state class graph, an information structure called a timed state observer is formulated to verify strong and weak detectability. The proposed verification technique is advantageous and is effectively applied to an intelligent garage system, since the enumeration of all states of the time-dependent system is not required. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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22 pages, 9285 KiB  

Open AccessArticle

A Control Method for Thermal Structural Tests of Hypersonic Missile Aerodynamic Heating

by Chao Lu, Guangming Zhang and Xiaodong Lv

Mathematics 2025, 13(3), 380; https://doi.org/10.3390/math13030380 - 24 Jan 2025

Viewed by 607

Abstract

This paper presents an intelligent proportional-derivative adaptive global nonsingular fast-terminal sliding-mode control (IPDAGNFTSMC) for tracking temperature trajectories of a hypersonic missile in thermal structural tests. Firstly, the numerical analyses on a hypersonic missile’s aerodynamic heating are based on three different external flow fields [...] Read more.

This paper presents an intelligent proportional-derivative adaptive global nonsingular fast-terminal sliding-mode control (IPDAGNFTSMC) for tracking temperature trajectories of a hypersonic missile in thermal structural tests. Firstly, the numerical analyses on a hypersonic missile’s aerodynamic heating are based on three different external flow fields via the finite element calculation, which provides the data basis for the thermal structural test of hypersonic vehicles; secondly, due to temperature trajectory differences of a hypersonic missile and the thermal inertia and nonlinear characteristics of quartz lamps in thermal structural test, IPDAGNFTSMC is proposed, consisting of three components: (i) the mathematical model of the thermal structural test is established and further replaced via an intelligent proportional-derivative with a nonlinear extended state observer (NESO) for online unknown disturbances observation; (ii) compared with the traditional sliding-mode control method, the AGNFTSMC method eliminates the reaching phase and the initial control state is trapped on the sliding-mode surface. Therefore, it can alleviate chattering phenomenon, accelerate the convergence rate of the sliding mode, and ensure that there is no singular problem in the entire control process; (iii) the adaptive law is designed to effectively solve problems of convergence stagnation and chattering phenomenon. The Lyapunov stability theory is used to prove the stability of the proposed IPDAGNFTSMC-NESO. Finally, the advantages of the designed control method are verified by experimental simulation and comparison. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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18 pages, 2009 KiB  

Open AccessArticle

Convergence Rates of Partial Truncated Numerical Algorithm for Stochastic Age-Dependent Cooperative Lotka–Volterra System

by Mengqing Zhang, Quanxin Zhu and Jing Tian

Symmetry 2024, 16(12), 1659; https://doi.org/10.3390/sym16121659 - 15 Dec 2024

Viewed by 645

Abstract

We present a numerical algorithm for a stochastic age-dependent cooperative Lotka–Volterra system that incorporates a partially truncated function. Since it is challenging to obtain the real solution for this system, and traditional numerical algorithms often experience blow-up phenomena, we design a partially truncated [...] Read more.

We present a numerical algorithm for a stochastic age-dependent cooperative Lotka–Volterra system that incorporates a partially truncated function. Since it is challenging to obtain the real solution for this system, and traditional numerical algorithms often experience blow-up phenomena, we design a partially truncated algorithm to ensure the solution remains well behaved. We further establish the convergence of the algorithm and obtain its convergence order. Finally, numerical simulations are presented to demonstrate our theoretical findings. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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24 pages, 7397 KiB  

Open AccessArticle

Solution of Fractional Differential Boundary Value Problems with Arbitrary Values of Derivative Orders for Time Series Analysis

by Dmitry Zhukov, Vadim Zhmud, Konstantin Otradnov and Vladimir Kalinin

Mathematics 2024, 12(24), 3905; https://doi.org/10.3390/math12243905 - 11 Dec 2024

Viewed by 619

Abstract

The paper considers the solution of a fractional differential boundary value problem, that is, a diffusion-type equation with arbitrary values of the derivative orders on an infinite axis. The difference between the obtained results and other authors’ ones is that these involve arbitrary [...] Read more.

The paper considers the solution of a fractional differential boundary value problem, that is, a diffusion-type equation with arbitrary values of the derivative orders on an infinite axis. The difference between the obtained results and other authors’ ones is that these involve arbitrary values of the derivative orders. The solutions described in the literature, as a rule, are considered in the case when the fractional time derivative β lies in the range: 0 < β ≤ 1, and the fractional state derivative α (the variable describing the state of the process) is in the range: 1 < α ≤ 2. The solution presented in the article allows us to consider any ranges for α and β, if the inequality 0 < β/α ≤ 0.865 is satisfied in the range β/α. In order to solve the boundary value problem, the probability density function of the observed state x of a certain process (for example, the magnitude of the deviation of the levels of a time series) from time t (for example, the time interval for calculating the amplitudes of the deviation of the levels of a time series) can be captured. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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23 pages, 11122 KiB  

Open AccessArticle

Numerical Investigation of Water Transport and Effective Electrical Conductivity in Perforation of Gas Diffusion Layer Using Lattice Boltzmann Method

by Jae Yong Cho, Hee Min Lee, Muhammad Nasir Bashir and Joon Sang Lee

Fractal Fract. 2024, 8(12), 719; https://doi.org/10.3390/fractalfract8120719 - 5 Dec 2024

Viewed by 899

Abstract

In polymer electrolyte membrane fuel cells, the gas diffusion layer (GDL) is composed of porous media and serves a critical role as a mass transport layer, facilitating reactant gas diffusion, removal of water generated in the catalyst layer, and electron transport. Artificial spacings [...] Read more.

In polymer electrolyte membrane fuel cells, the gas diffusion layer (GDL) is composed of porous media and serves a critical role as a mass transport layer, facilitating reactant gas diffusion, removal of water generated in the catalyst layer, and electron transport. Artificial spacings known as perforations can be introduced to improve water management within this mass transport system. However, the impact of these perforations on the effective electrical conductivity has not been adequately studied. This study employs numerical methods to investigate water management and effective electrical conductivity in the presence of perforations, aiming to provide indicators for optimal design. The pseudopotential lattice Boltzmann method is utilized, which is particularly advantageous for modeling two-phase flow and electron transport in complex geometries. Using this numerical approach, we analyze water penetration in GDL structures and effective electrical conductivity based on electric potential fields focusing on geometric parameters such as the perforation size. Our results demonstrate a relationship between water management efficiency and effective electrical conductivity, suggesting the existence of an optimal perforation diameter. Moreover, when there is a water-induced penetration pattern due to the perforated structure, both the effective electrical conductivity and water management are enhanced at a lower porosity of the GDL structure. Full article

(This article belongs to the Topic Modeling, Stability, and Control of Dynamic Systems and Their Applications)

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