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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 31 December 2026 | Viewed by 20164

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Prof. Dr. Adrian Olaru

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Department of Robotics and Production Systems, University Politehnica of Bucharest, 060042 Bucharest, Romania
Interests: robotics; dynamic behavior; neural networks; mobile robots; neurorehabilitation
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Prof. Dr. Gabriel Frumusanu

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Manufacturing Science and Engineering Department, “Dunarea de Jos” University of Galati, 800201 Galati, Romania
Interests: numerical modeling of machining systems; manufacturing process control; dynamics of cutting processes; chaos theory; computer-assisted design
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Prof. Dr. Catalin Alexandru

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Department of Product Design, Mechatronics and Environment, Transilvania University of Brasov, 500036 Brasov, Romania
Interests: mechanical systems; renewable energy systems; virtual prototyping; modeling and simulation
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Special Issue Information

Dear Colleagues,

This Special Issue titled “Dynamic Modeling and Simulation for Control Systems, Third Edition”, as a follow-up to the successful first edition and second edition, will provide a comprehensive platform for researchers and practitioners to explore topics related to the dynamic modeling, simulation, and optimization of control systems in various engineering fields. Specifically, this Special Issue aims to cover important aspects of how to optimize the dynamic behavior of physical systems using special algorithms and artificial intelligence in the modeling, simulation, and optimization of the components and systems across diverse engineering disciplines, such as astronautics, aerospace, avionics, robotics, manufacturing systems, mechanical engineering, power energy, materials technology, and neurorehabilitation.

Topics for this Special Issue:

Mathematical modeling of control systems;
Control of physical engineering systems;
Optimization algorithms in engineering systems;
Design of physical engineering systems;
Mechanical, electrical, and fluid interaction between system components;
Dynamic behavior analysis;
System response analysis;
Feedback control systems;
Numerical simulation of integrated systems;
Fault detection and diagnosis;
Networked control and time-delay systems;
Frequency response and stability;
Control and simulation of the isotope separation process;
Fuzzy logic and control systems;
Neural network applied in complex control systems;
Artificial intelligence and support vector machine for control systems.

This Special Issue of Mathematics will be a useful guide on techniques for the modeling, simulation, and optimization of control systems to obtain acceptable dynamic behaviors.

Prof. Dr. Adrian Olaru
Prof. Dr. Gabriel Frumusanu
Prof. Dr. Catalin Alexandru
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 250 words) can be sent to the Editorial Office for assessment.

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

mathematical modeling
numerical simulation
optimization algorithms
control systems
time response analysis
time-delay systems
feedback control
networked control
stochastic control
fault detection
robust control
adaptive control
frequency response analysis
stability analysis
fuzzy logic
data acquisition
neural networks
artificial intelligence
mechanical and electrical interaction
physical engineering design

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Related Special Issue

Dynamic Modeling and Simulation for Control Systems, 2nd Edition in Mathematics (10 articles)

Published Papers (11 papers)

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Research

24 pages, 3302 KB

Open AccessArticle

Lyapunov-Based Event-Triggered Fault-Tolerant Distributed Control for DC Microgrids with Communication Failures

by Ilhami Poyraz, Heybet Kilic and Mehmet Emin Asker

Mathematics 2026, 14(7), 1152; https://doi.org/10.3390/math14071152 - 30 Mar 2026

Viewed by 409

Abstract

Recently, distributed DC microgrids have gained prominence due to their modular design, scalability, and seamless integration with renewable energy sources. However, ensuring robust operation of distributed secondary control schemes remains challenging, particularly in the presence of unavoidable communication disruptions and parametric uncertainties encountered in practice. Most existing control strategies either assume ideal communication networks or address fault tolerance and communication constraints separately, which limits their applicability in realistic networked environments. This paper proposes an event-triggered fault-tolerant distributed secondary control framework for DC microgrids operating under communication faults. An embedded averaged model is incorporated to support fault-tolerant decision-making and to guide event-triggered communication updates. In addition, an auxiliary recovery mechanism is introduced, enabling neighboring converters to cooperatively compensate for information loss during communication interruptions without centralized supervision. Lyapunov-based stability analysis establishes boundedness and practical convergence of the closed-loop system under event-triggered updates and bounded disturbances while explicitly excluding Zeno behavior. The simulation results under communication fault scenarios demonstrate that the proposed approach achieves accurate DC bus voltage regulation with steady-state deviations below 1% while restoring proportional power sharing with an averaged error within 5%. The embedded model error remains bounded throughout the fault interval, and fault-tolerant control actions are triggered sparsely with well-separated inter-event times on the order of tens of milliseconds, thereby significantly reducing the communication burden. These results confirm the effectiveness and robustness of the proposed framework for the resilient operation of distributed DC microgrids under practical communication constraints. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)

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22 pages, 803 KB

Open AccessArticle

Hierarchical Reinforcement Learning–Based Optimal Control for Model-Free Linear Systems

by Yong Zhang, Xiangrui Yan, Weiqing Yang and Yuyang Zhou

Mathematics 2026, 14(5), 895; https://doi.org/10.3390/math14050895 - 6 Mar 2026

Viewed by 558

Abstract

A novel model-free hierarchical reinforcement learning (HRL)–based Linear Quadratic Regulator (LQR) control framework with adaptive weight selection is proposed to address the reliance of conventional LQR methods on accurate system models and manual parameter tuning. The proposed approach adopts a two-level learning architecture in which a high-level meta-agent adaptively optimizes the LQR weighting matrices Q and R through entropy-based trajectory evaluation, while a low-level base-agent performs model-free policy iteration to update the state-feedback control law under unknown system dynamics. By decoupling weight optimization from control-law learning, the framework enables simultaneous adaptation of the cost-function parameters and the feedback gain without requiring explicit model information. To enhance learning stability and exploration during weight adaptation, Gaussian noise and an experience replay mechanism are incorporated into the learning process. Numerical simulations on second- and third-order linear systems demonstrate that the proposed HRL-based LQR method achieves effective control performance, reliable convergence, and improved adaptability in model-free environments. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)

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17 pages, 1105 KB

Open AccessArticle

On Non-Commensurate Fractional-Order System Control

by Mircea Ivanescu and Decebal Popescu

Mathematics 2026, 14(5), 887; https://doi.org/10.3390/math14050887 - 5 Mar 2026

Viewed by 329

Abstract

The control systems for models described by non-commensurate fractional-order differential equations are based on their transformation into large commensurate-order systems, which impose difficulties in determining control laws. In this context, in this paper, a new control method for this class of systems is proposed. The results obtained are based on Lyapunov methods for differential equations with fractional exponents and on the application of the Yakubovich–Kalman–Popov lemma adapted for this class of systems. The stability criterion is presented as a frequency criterion and represented graphically by familiar frequency plots similar to those of the Nyquist or Popov type. If the parameters that define the model can be defined in a closed domain, the frequency criterion can be interpreted as “Popov’s circle criterion”. The two numerical applications present two important cases. The first studies the stability criterion in the case where the viscosity coefficients determine non-commensurate fractional-order exponents in the dynamic model of the system. The second example studies the complex problem of the human–machine system in which the human model imposes dynamics determined by non-commensurate fractional-order systems. The proposed investigation methods allow for a reduction in computational effort by several orders of magnitude for non-commensurate fractional-order systems, eliminate stability conditions that use matrix-based criteria for large-scale systems, and introduce standard frequency-domain criteria. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)

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22 pages, 2938 KB

Open AccessArticle

Establishment and Analysis of a General Mass Model for Solenoid Valves Used in Space Propulsion Systems

by Yezhen Sun, Sen Hu and Guozhu Liang

Mathematics 2026, 14(1), 106; https://doi.org/10.3390/math14010106 - 27 Dec 2025

Viewed by 567

Abstract

The solenoid valve component is the core part affecting the total mass of space propulsion system, and the accuracy of the solenoid valve mass model directly impacts the accuracy of the system mass estimation and optimization design. This study focuses on the solenoid valves used in gas path control for cold gas propulsion systems. The relationship between the gas flow rate and volume flow rate of the solenoid valve is derived. By analyzing the parameters affecting the mass of the solenoid valves, a general calculation mass model of the gas solenoid valve used in cold gas propulsion is proposed based on strength theory. Combining with the existing general calculation mass model for liquid solenoid valves and collecting mass data of 16 gas solenoid valves and 33 liquid solenoid valves used in space propulsion system, the mass calculation formulas of the gas and liquid solenoid valves are obtained by employing several mathematical fitting methods, including quadratic polynomial surface, Manski formula, bivariate power function, and pressure-corrected polynomial. The accuracy of different mass model formulas is compared to assess their performance in calculating the solenoid valve mass. The results show that the quadratic surface formula can better reflect the relationship between the mass of the gas solenoid valves and the valve parameters within the medium volume flow range of 1 × 10⁻⁹ to 3.9 × 10⁻³ m³/s and the proof pressure range of 0.4 to 49.74 MPa. For the calculation of liquid solenoid valve mass, the accuracy of quadratic polynomial surface fitting, bivariate power function equation, and univariate polynomial equation with pressure correction is comparable within the liquid volume flow range of 1.8 × 10⁻⁷ to 1.28 × 10⁻⁴ m³/s and the inlet pressure range of 0.99 to 4.24 MPa; the appropriate calculation formula can be selected based on the pressure conditions in the liquid solenoid valve chamber in practical applications. Sensitivity analysis shows a consistent trend for gas and liquid solenoid valves: proof pressure (gas valves) or inlet working pressure (liquid valves) are the dominant factors affecting valve mass, while volume flow rate has a moderate impact. The proposed solenoid valve mass model in this study can be used to calculate the mass of gas solenoid valves for space cold gas propulsion systems and liquid solenoid valves for liquid rocket thrusters with thrust below 1000 N, providing an important reference for the mass modeling and optimization design of the space propulsion systems. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)

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32 pages, 7592 KB

Open AccessEditor’s ChoiceArticle

Backstepping Sliding Mode Control of Quadrotor UAV Trajectory

by Yohannes Lisanewerk Mulualem, Gang Gyoo Jin, Jaesung Kwon and Jongkap Ahn

Mathematics 2025, 13(19), 3205; https://doi.org/10.3390/math13193205 - 6 Oct 2025

Cited by 1 | Viewed by 1581

Abstract

Unmanned Aerial Vehicles (UAVs), commonly known as drones, have become widely used in many fields, ranging from agriculture to military operations, due to recent advances in technology and decreases in costs. Quadrotors are particularly important UAVs, but their complex, coupled dynamics and sensitivity to outside disturbances make them challenging to control. This paper introduces a new control method for quadrotors called Backstepping Sliding Mode Control (BSMC), which combines the strengths of two established techniques: Backstepping Control (BC) and Sliding Mode Control (SMC). Its primary goal is to improve trajectory tracking while also reducing chattering, a common problem with SMC that causes rapid, high-frequency oscillations. The BSMC method achieves this by integrating the SMC switching gain directly into the BC through a process of differential iteration. Herein, a Lyapunov stability analysis confirms the system’s asymptotic stability; a genetic algorithm is used to optimize controller parameters; and the proposed control strategy is evaluated under diverse payload conditions and dynamic wind disturbances. The simulation results demonstrated its capability to handle payload variations ranging from 0.5 kg to 18 kg in normal environments, and up to 12 kg during gusty wind scenarios. Furthermore, the BSMC effectively minimized chattering and achieved a superior performance in tracking accuracy and robustness compared to the traditional SMC and BC. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)

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12 pages, 808 KB

Open AccessArticle

Robust Angular Frequency Control of Incommensurate Fractional-Order Permanent Magnet Synchronous Motors via State-Sequential Sliding Mode Control

by Guo-Hsin Hu, Chia-Wei Ho and Jun-Juh Yan

Mathematics 2025, 13(16), 2669; https://doi.org/10.3390/math13162669 - 19 Aug 2025

Cited by 1 | Viewed by 745

Abstract

This paper proposes an innovative state-sequential sliding mode control (SS-SMC) to suppress chaotic behavior and achieve angular frequency control of incommensurate fractional-order permanent magnet synchronous motor (IFOPMSM) systems. The method is designed to handle both input perturbations and mismatched external disturbances. Conventional sliding mode control (SMC) is robust to matched uncertainties. However, the use of discontinuous sign functions causes chattering. This reduces control accuracy and overall performance. Many methods have been proposed to reduce chattering. Yet, for IFOPMSMs, achieving both robust stabilization and chattering suppression under mismatched disturbances and input uncertainties remains challenging. To address these issues, this study introduces an SS-SMC strategy that combines a fractional-order integral-type sliding surface with a continuous control law. Unlike conventional SMC methods that rely on discontinuous sign functions, the proposed approach uses a continuous control function. This preserves the robustness of traditional SMC while effectively eliminating chattering. The SS-SMC utilizes state-sequential control, allowing a single input to stabilize all system states sequentially and achieve the control objectives while reducing system complexity. Simulation results and comparative analyses confirm the effectiveness of the proposed method. The findings show that the SS-SMC ensures robust angular frequency regulation of the IFOPMSM and suppresses chattering effectively. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)

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28 pages, 4927 KB

Open AccessArticle

Hybrid Genetic Algorithm-Based Optimal Sizing of a PV–Wind–Diesel–Battery Microgrid: A Case Study for the ICT Center, Ethiopia

by Adnan Kedir Jarso, Ganggyoo Jin and Jongkap Ahn

Mathematics 2025, 13(6), 985; https://doi.org/10.3390/math13060985 - 17 Mar 2025

Cited by 12 | Viewed by 3439

Abstract

This study presents analysis and optimization of a standalone hybrid renewable energy system (HRES) for Adama Science and Technology University’s ICT center in Ethiopia. The proposed hybrid system combines photovoltaic panels, wind turbines, a battery bank, and a diesel generator to ensure reliable and sustainable power. The objectives are to minimize the system’s total annualized cost and loss of power supply probability, while energy reliability is maintained. To optimize the component sizing and energy management strategy of the HRES, we formulated a mathematical model that incorporates the variability of renewable energy and load demand. This optimization problem is solved using a hybrid genetic algorithm (HGA). Simulation results indicate that the HGA yielded the best solution, characterized by the levelized cost of energy of USD 0.2546/kWh, the loss of power supply probability of 0.58%, and a convergence time of 197.2889 s. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)

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19 pages, 3164 KB

Open AccessArticle

Application of Real-Coded Genetic Algorithm–PID Cascade Speed Controller to Marine Gas Turbine Engine Based on Sensitivity Function Analysis

by Yunhyung Lee, Kitak Ryu, Gunbaek So, Jaesung Kwon and Jongkap Ahn

Mathematics 2025, 13(2), 314; https://doi.org/10.3390/math13020314 - 19 Jan 2025

Cited by 3 | Viewed by 1613

Abstract

Gas turbine engines at sea, characterized by nonlinear behavior and parameter variations due to dynamic marine environments, pose challenges for precise speed control. The focus of this study was a COGAG system with four LM-2500 gas turbines. A third-order model with time delay was derived at three operating points using commissioning data to capture the engines’ inherent characteristics. The cascade controller design employs a real-coded genetic algorithm–PID (R-PID) controller, optimizing PID parameters for each model. Simulations revealed that the R-PID controllers, optimized for robustness, show Nyquist path stability, maintaining the furthest distance from the critical point (−1, j0). The smallest sensitivity function

M s

(maximum sensitivity) values and minimal changes in

M s

for uncertain plants confirm robustness against uncertainties. Comparing transient responses, the R-PID controller outperforms traditional methods like IMC and Sadeghi in total variation in control input, settling time, overshoot, and ITAE, despite a slightly slower rise time. However, controllers designed for specific operating points show decreased performance when applied beyond those points, with increased rise time, settling time, and overshoot, highlighting the need for operating-point-specific designs to ensure optimal performance. This research underscores the importance of tailored controller design for effective gas turbine engine management in marine applications. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)

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17 pages, 949 KB

Open AccessArticle

Adaptive Control for Multi-Agent Systems Governed by Fractional-Order Space-Varying Partial Integro-Differential Equations

by Zhen Liu, Yingying Wen, Bin Zhao and Chengdong Yang

Mathematics 2025, 13(1), 112; https://doi.org/10.3390/math13010112 - 30 Dec 2024

Cited by 1 | Viewed by 1398

Abstract

This paper investigates a class of multi-agent systems (MASs) governed by nonlinear fractional-order space-varying partial integro-differential equations (SVPIDEs), which incorporate both nonlinear state terms and integro terms. Firstly, a distributed adaptive control protocol is developed for leaderless fractional-order SVPIDE-based MASs, aiming to achieve consensus among all agents without a leader. Then, for leader-following fractional-order SVPIDE-based MASs, the protocol is extended to account for communication between the leader and follower agents, ensuring that the followers reach consensus with the leader. Finally, three examples are presented to illustrate the effectiveness of the proposed distributed adaptive control protocols. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)

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13 pages, 1145 KB

Open AccessArticle

Distributed Bipartite Consensus of Multi-Agent Systems via Disturbance Rejection Control Strategy

by Subramanian Manickavalli, Arumugam Parivallal, Ramasamy Kavikumar and Boomipalagan Kaviarasan

Mathematics 2024, 12(20), 3225; https://doi.org/10.3390/math12203225 - 15 Oct 2024

Cited by 4 | Viewed by 2502

Abstract

This work aims to focus on analyzing the consensus control problem in cooperative–competitive networks in the occurrence of external disturbances. The primary motive of this work is to employ the equivalent input-disturbance estimation technique to compensate for the impact of external disturbances in the considered multi-agent system. In particular, a suitable low-pass filter is implemented to enhance the accuracy of disturbance estimation performance. In addition, a specific signed, connected, and structurally balanced undirected communication graph with positive and negative edge weights is considered to express the cooperation–competition communication among neighboring agents. The cooperative–competitive multi-agent system reaches its final state with same magnitude and in opposite direction under the considered structurally balanced graph. By utilizing the properties of Lyapunov stability theory and graph theory, the adequate conditions assuring the bipartite consensus of the examined multi-agent system are established as linear matrix inequalities. An illustrative example is delivered at the end to check the efficacy of the designed control scheme. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)

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17 pages, 3678 KB

Open AccessArticle

Electric Vehicle Motor Fault Detection with Improved Recurrent 1D Convolutional Neural Network

by Prashant Kumar, Prince, Ashish Kumar Sinha and Heung Soo Kim

Mathematics 2024, 12(19), 3012; https://doi.org/10.3390/math12193012 - 26 Sep 2024

Cited by 9 | Viewed by 3352

Abstract

The reliability of electric vehicles (EVs) is crucial for the performance and safety of modern transportation systems. Electric motors are the driving force in EVs, and their maintenance is critical for efficient EV performance. The conventional fault detection methods for motors often struggle with accurately capturing complex spatiotemporal vibration patterns. This paper proposes a recurrent convolutional neural network (RCNN) for effective defect detection in motors, taking advantage of the advances in deep learning techniques. The proposed approach applies long short-term memory (LSTM) layers to capture the temporal dynamics essential for fault detection and convolutional neural network layers to mine local features from the segmented vibration data. This hybrid method helps the model to learn complicated representations and correlations within the data, leading to improved fault detection. Model development and testing are conducted using a sizable dataset that includes various kinds of motor defects under differing operational scenarios. The results demonstrate that, in terms of fault detection accuracy, the proposed RCNN-based strategy performs better than the traditional fault detection techniques. The performance of the model is assessed under varying vibration data noise levels to further guarantee its effectiveness in practical applications. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)

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