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Mathematics
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Modeling, Simulation and Control of Dynamical Systems
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Modeling, Simulation and Control of Dynamical Systems

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

Deadline for manuscript submissions: 30 June 2025 | Viewed by 8628

Special Issue Editors

Dr. Humam Al-Baidhani

E-Mail Website
Guest Editor
Department of Electrical Engineering, Wright State University, Dayton, OH 45435, USA
Interests: DC-DC converters; modeling and control; nonlinear systems
Prof. Dr. Marian K. Kazimierczuk

E-Mail Website
Guest Editor
Department of Electrical Engineering, Wright State University, Dayton, OH 45435-0001, USA
Interests: modeling and control; resonant converters; RF power amplifiers; magnetics; industrial electronics

Special Issue Information

Dear Colleagues,

Dynamical systems arise in various engineering fields, including electrical, mechanical, civil, and control engineering areas. In order to study and characterize the systems that involve dynamic processes, mathematical modeling and simulation are required. Such engineering tools play a vital role in understanding the system behavior, designing a suitable control law, and analyzing the system’s stability. The design of proper control schemes is essential to track the desired trajectory and improve the system dynamics. However, in real-world applications, the nonlinearities, modeling uncertainties, and external disturbances can complicate the modeling and control design tasks. Hence, advanced approaches are required to design robust control schemes and provide rigorous analysis to ensure the stability of the closed-loop control systems.

In this context, this Special Issue aims to collect state-of-the-art research contributions on the modeling, simulation, and control of dynamical systems. Accurate models and advanced control techniques of nonlinear systems that resolve practical control design issues are encouraged.

Potential topics include, but are not limited to, the following:

  1. Stability analysis of dynamical systems;
  2. Real-time and HIL simulation; 
  3. Control and analysis of nonlinear systems;
  4. Modeling and control of power converters;
  5. Digital control system design and applications;
  6. Artificial intelligence in controls and robotics;
  7. Tracking and disturbance rejection enhancement;
  8. Design and optimization of PV systems;
  9. Simulation and control in aerospace.

Dr. Humam Al-Baidhani
Prof. Dr. Marian K. Kazimierczuk
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 systems
  • modeling and simulation
  • nonlinear systems
  • stability analysis

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Published Papers (6 papers)

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Research

24 pages, 341 KiB  
Article
Almost k-Step Opacity Enforcement in Stochastic Discrete-Event Systems via Differential Privacy
by Rong Zhao, Murat Uzam and Zhiwu Li
Mathematics 2025, 13(8), 1255; https://doi.org/10.3390/math13081255 - 10 Apr 2025
Viewed by 242
Abstract
This paper delves into current-state opacity enforcement in partially observed discrete event systems through an innovative application of differential privacy, which is fundamental for security-critical cyber–physical systems. An opaque system implies that an external agent cannot infer the predefined system secret via its [...] Read more.
This paper delves into current-state opacity enforcement in partially observed discrete event systems through an innovative application of differential privacy, which is fundamental for security-critical cyber–physical systems. An opaque system implies that an external agent cannot infer the predefined system secret via its observational output, such that the important system information flow cannot be leaked out. Differential privacy emerges as a robust framework that is pivotal for the protection of individual data integrity within these systems. Motivated by the differential privacy mechanism for information protection, this research proposes the secret string adjacency relation as a novel concept, assessing the similarity between potentially compromised strings and system-generated alternatives, thereby shielding the system’s confidential data from external observation. The development of secret string differential privacy is achieved by substituting sensitive strings. These substitution strings are generated by a modified Levenshtein automaton, following exponentially distributed generation probabilities. The verification and illustrative examples of the proposed mechanism are provided. Full article
(This article belongs to the Special Issue Modeling, Simulation and Control of Dynamical Systems)
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17 pages, 1487 KiB  
Article
A Novel Nonlinear Adaptive Control Method for Longitudinal Speed Control for Four-Independent-Wheel Autonomous Vehicles
by Jinhua Zhang, Zhenghao Chen and Jinshi Yu
Mathematics 2024, 12(22), 3509; https://doi.org/10.3390/math12223509 - 9 Nov 2024
Viewed by 1139
Abstract
As autonomous driving technology and four-independent-wheel chassis systems advance, four-independent-wheel autonomous vehicles have increasingly become a focal area of modern research. The longitudinal control problem for four-independent-wheel autonomous vehicles presents challenges such as complex models, high nonlinearity, and strong system uncertainties. This paper [...] Read more.
As autonomous driving technology and four-independent-wheel chassis systems advance, four-independent-wheel autonomous vehicles have increasingly become a focal area of modern research. The longitudinal control problem for four-independent-wheel autonomous vehicles presents challenges such as complex models, high nonlinearity, and strong system uncertainties. This paper proposes a novel hierarchical control algorithm to address these challenges, innovatively combining the advantages of adaptive backstepping and dynamic sliding mode control algorithms in the upper controller, allowing it to effectively overcome the impact of uncertain system parameters and suppress the common chattering phenomenon in the output of typical sliding mode control methods. Based on the design of the upper controller, an innovative optimized longitudinal force distribution strategy and the construction of a tire reverse longitudinal slip model are proposed, followed by the design of a fuzzy PID controller as the lower slip ratio controller to achieve precise whole-vehicle longitudinal speed tracking and improve overall control performance. This method not only improves the accuracy of speed tracking but also enhances the robustness and adaptability of the control system. Finally, the effectiveness and superiority of the proposed hierarchical control method are verified through CarSim simulations. Full article
(This article belongs to the Special Issue Modeling, Simulation and Control of Dynamical Systems)
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19 pages, 5928 KiB  
Article
Design and Implementation of Digital PID Control for Mass-Damper Rectilinear Systems
by Humam Al-Baidhani and Marian K. Kazimierczuk
Mathematics 2024, 12(18), 2921; https://doi.org/10.3390/math12182921 - 20 Sep 2024
Cited by 1 | Viewed by 1287
Abstract
The mechanical systems were modeled using various combinations of mass-damper-spring elements to analyze the system dynamics and improve the system stability. Due to the marginal stability property of the mass-damper rectilinear system, a proper control law is required to control the mass position [...] Read more.
The mechanical systems were modeled using various combinations of mass-damper-spring elements to analyze the system dynamics and improve the system stability. Due to the marginal stability property of the mass-damper rectilinear system, a proper control law is required to control the mass position accurately, improve the relative stability, and enhance the dynamical response. In this paper, a mathematical model of the electromechanical system was first derived and analyzed. Next, a digital PID controller was developed based on the root locus technique, and a systematic design procedure is presented in detail. The proposed digital control system was simulated in MATLAB and compared with other control schemes to check their tracking performance and transient response characteristics. In addition, the digital PID control algorithm of the mass-damper rectilinear system was implemented via dSPACE platform to investigate the real-time control system performance and validate the control design methodology. It has been shown that the digital PID controller yields zero percentage overshoot, fast transient response, adequate stability margins, and zero steady-state error. Full article
(This article belongs to the Special Issue Modeling, Simulation and Control of Dynamical Systems)
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23 pages, 7505 KiB  
Article
Dynamic Analysis and PD Control in a 12-Pole Active Magnetic Bearing System
by Yigen Ren and Wensai Ma
Mathematics 2024, 12(15), 2331; https://doi.org/10.3390/math12152331 - 25 Jul 2024
Cited by 3 | Viewed by 1123
Abstract
This paper conducts an in-depth study on the dynamic stability and complex vibration behavior of a 12-pole active magnetic bearing (AMB) system considering gravitational effects under a PD controller. Firstly, based on electromagnetic theory and Newton’s second law, a two-degree-of-freedom control equation of [...] Read more.
This paper conducts an in-depth study on the dynamic stability and complex vibration behavior of a 12-pole active magnetic bearing (AMB) system considering gravitational effects under a PD controller. Firstly, based on electromagnetic theory and Newton’s second law, a two-degree-of-freedom control equation of the system, including PD control terms and gravitational effects, is constructed. This equation involves not only parametric excitation, quadratic nonlinearity, and cubic nonlinearity but also a more pronounced coupling effect between the magnetic poles due to the presence of gravity. Secondly, using the multi-scale method, a four-dimensional averaged equation of the system in Cartesian and polar coordinates is derived. Finally, through numerical analysis, the system’s amplitude–frequency response, motion trajectory, the relationship between energy and amplitude, and global dynamic behaviors such as bifurcation and chaos are discussed in detail. The results show that the PD controller significantly affects the system’s spring hardening/softening characteristics, excitation, amplitude, energy, and stability. Specifically, increasing the proportional gain can quickly suppress the rotor’s motion, but it also increases the system’s instability. Adjusting the differential gain can transition the system from a chaotic state to a stable periodic motion. Full article
(This article belongs to the Special Issue Modeling, Simulation and Control of Dynamical Systems)
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15 pages, 4676 KiB  
Article
Numerical Investigation of Supersonic Flow over a Wedge by Solving 2D Euler Equations Utilizing the Steger–Warming Flux Vector Splitting (FVS) Scheme
by Mitch Wolff, Hashim H. Abada and Hussein Awad Kurdi Saad
Mathematics 2024, 12(9), 1282; https://doi.org/10.3390/math12091282 - 24 Apr 2024
Cited by 2 | Viewed by 1533
Abstract
Supersonic flow over a half-angle wedge (θ = 15°) with an upstream Mach number of 2.0 was investigated using 2D Euler equations where sea level conditions were considered. The investigation employed the Steger–Warming flux vector splitting (FVS) method executed in MATLAB 9.13.0 (R2022b) [...] Read more.
Supersonic flow over a half-angle wedge (θ = 15°) with an upstream Mach number of 2.0 was investigated using 2D Euler equations where sea level conditions were considered. The investigation employed the Steger–Warming flux vector splitting (FVS) method executed in MATLAB 9.13.0 (R2022b) software. The study involved a meticulous comparison between theoretical calculations and numerical results. Particularly, the research emphasized the angle of oblique shock and downstream flow properties. A substantial iteration count of 2000 iteratively refined the outcomes, underscoring the role of advanced computational resources. Validation and comparative assessment were conducted to elucidate the superiority of the Steger–Warming flux vector splitting (FVS) scheme over existing methodologies. This research serves as a link between theoretical rigor and practical applications in high-speed aerospace design, enhancing the efficiency of aircraft components. Full article
(This article belongs to the Special Issue Modeling, Simulation and Control of Dynamical Systems)
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22 pages, 1024 KiB  
Article
Reinforcement Learning-Based Control of a Power Electronic Converter
by Dajr Alfred, Dariusz Czarkowski and Jiaxin Teng
Mathematics 2024, 12(5), 671; https://doi.org/10.3390/math12050671 - 25 Feb 2024
Cited by 7 | Viewed by 2579
Abstract
This article presents a modern, data-driven, reinforcement learning-based (RL-based), discrete-time control methodology for power electronic converters. Additionally, the key advantages and disadvantages of this novel control method in comparison to classical frequency-domain-derived PID control are examined. One key advantage of this technique is [...] Read more.
This article presents a modern, data-driven, reinforcement learning-based (RL-based), discrete-time control methodology for power electronic converters. Additionally, the key advantages and disadvantages of this novel control method in comparison to classical frequency-domain-derived PID control are examined. One key advantage of this technique is that it obviates the need to derive an accurate system/plant model by utilizing measured data to iteratively solve for an optimal control solution. This optimization algorithm stems from the linear quadratic regulator (LQR) and involves the iterative solution of an algebraic Riccati equation (ARE). Simulation results implemented on a buck converter are provided to verify the effectiveness and examine the limitations of the proposed control strategy. The implementation of a classical Type-III compensator was also simulated to serve as a performance comparison to the proposed controller. Full article
(This article belongs to the Special Issue Modeling, Simulation and Control of Dynamical Systems)
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