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20 pages, 993 KiB

Open AccessArticle

Calculus of Long Rectangular Plates Embedded in Long Borders with Uniform Vertical Load on a Line Parallel to the Long Borders

by Daniel Opruţa, Mihai-Sorin Tripa, Luminiţa Codrea, Cristian Boldor, Dan Dumea, Robert Gyorbiro, Cosmin Brisc, Iulia Bărăian, Petre Opriţoiu, Aurel Chereches and Mihaela Suciu

Mathematics 2025, 13(6), 993; https://doi.org/10.3390/math13060993 - 18 Mar 2025

Viewed by 192

Abstract

This article presents the Transfer Matrix Method as a mathematical approach for the calculus of different structures that can be discretized into elements using an iterative calculus for future applications in the vehicle industry. Plate calculus is important in construction, medicine, orthodontics, and [...] Read more.

This article presents the Transfer Matrix Method as a mathematical approach for the calculus of different structures that can be discretized into elements using an iterative calculus for future applications in the vehicle industry. Plate calculus is important in construction, medicine, orthodontics, and many other fields. This work is original due to the mathematical apparatus used in the calculus of long rectangular plates embedded in both long borders and required by a uniformly distributed force on a line parallel to the long borders. The plate is discretized along its length in unitary beams, which have the width of the rectangular plate. The unitary beam can also be discretized into parts. As applications, the long rectangular plates embedded on the two long borders and charged with a vertical uniform load that acts on a line parallel to the long borders are studied. A state vector is associated with each side. For each of the four cases studied, a matrix relationship was written for each side, based on a transfer matrix, the state vector corresponding to the origin side, and the vector due to the action of external forces acting on the considered side. After, it is possible to calculate all the state vectors for all sides of the unity beam. Now, the efforts, deformations, and stress can be calculated in any section of the beam, respectively, for the long rectangular plate. This calculus will serve as a calculus of resistance for different pieces of the components of vehicles. Full article

(This article belongs to the Special Issue Control Theory and Applications, 2nd Edition)

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14 pages, 898 KiB

Open AccessArticle

About Calculus Through the Transfer Matrix Method of a Beam with Intermediate Support with Applications in Dental Restorations

by Otilia Cojocariu-Oltean, Mihai-Sorin Tripa, Iulia Bărăian, Doina-Iulia Rotaru and Mihaela Suciu

Mathematics 2024, 12(23), 3861; https://doi.org/10.3390/math12233861 - 8 Dec 2024

Cited by 2 | Viewed by 803

Abstract

This work presents an original and very interesting approach to a calculus problem involving beams with intermediate supports through the transfer-matrix method, a very easy method to program to quickly obtain good results. To exemplify the applicability of this approach in dentistry, the [...] Read more.

This work presents an original and very interesting approach to a calculus problem involving beams with intermediate supports through the transfer-matrix method, a very easy method to program to quickly obtain good results. To exemplify the applicability of this approach in dentistry, the calculus of a dental bridge on three poles is explored. Dental restorations are very important for improving a person’s general state of health as a result of improving mastication and esthetic appearance. The approach used in this study consists of presenting a theoretical study about an indeterminate beam with an intermediate support and then particularizing it for application in a dental restoration case, with a dental bridge on three poles and two missing teeth between the three poles. The bridge is assimilated to a simple static indeterminate beam. This paper is unique in that it involves the application of the transfer-matrix method for a case study in dental restoration. The assimilation of a dental bridge with a statically undetermined beam, resting on the extremities and on an intermediate support, is an original approach. The results obtained in the presented case study were validated by comparison with those obtained through the classical calculation of the Resistance of Materials, with Clapeyron’s equation of three moments. Due to the ease and elegance of solving various problems with the TMM, this approach will continue to be relevant to other original case studies with different modeling requirements, and these applications will be presented in future research. Full article

(This article belongs to the Special Issue Control Theory and Applications, 2nd Edition)

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18 pages, 6661 KiB

Open AccessArticle

On Neural Observer in Dynamic Sliding Mode Control of Permanent Magnet Synchronous Wind Generator

by Ali Karami-Mollaee and Oscar Barambones

Mathematics 2024, 12(14), 2246; https://doi.org/10.3390/math12142246 - 19 Jul 2024

Cited by 1 | Viewed by 809

Abstract

The captured energy of a wind turbine (WT) can be converted into electricity by a generator. Therefore, to improve the efficiency of this system, both the structures of WTs and generators should be considered for control. But the present challenge is WT uncertainty, [...] Read more.

The captured energy of a wind turbine (WT) can be converted into electricity by a generator. Therefore, to improve the efficiency of this system, both the structures of WTs and generators should be considered for control. But the present challenge is WT uncertainty, while the input signals to the generator should be smooth. In this paper, a permanent magnet synchronous generator (PMSG) is considered. The dynamics of the PMSG can be described using two axes, named d-q reference frameworks, with an input in each framework direction. To obtain the maximum power and to overcome the uncertainty by means of a smooth signal, the dynamic sliding mode controller (D-SMC) is implemented. In the D-SMC, an integrator is placed in the control scheme in order to suppress the chattering, because it acts like a low-pass filter. To estimate the state added by the integrator, a new observer-based neural network (ONN) is proposed. The proof of the stability of the D-SMC and ONN is based on Lyapunov theory. To prove the advantages of the D-SMC, a comparison was also carried out by traditional sliding mode control (T-SMC) with a similar ONN. From this comparison, we know that the advantages of the D-SMC are clear in terms of real implementation, concept, and chattering suppression. Full article

(This article belongs to the Special Issue Control Theory and Applications, 2nd Edition)

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15 pages, 321 KiB

Open AccessArticle

Saddle-Point Equilibrium Strategy for Linear Quadratic Uncertain Stochastic Hybrid Differential Games Based on Subadditive Measures

by Zhifu Jia and Cunlin Li

Mathematics 2024, 12(8), 1132; https://doi.org/10.3390/math12081132 - 9 Apr 2024

Viewed by 1289

Abstract

This paper describes a kind of linear quadratic uncertain stochastic hybrid differential game system grounded in the framework of subadditive measures, in which the system dynamics are described by a hybrid differential equation with Wiener–Liu noise and the performance index function is quadratic. [...] Read more.

This paper describes a kind of linear quadratic uncertain stochastic hybrid differential game system grounded in the framework of subadditive measures, in which the system dynamics are described by a hybrid differential equation with Wiener–Liu noise and the performance index function is quadratic. Firstly, we introduce the concept of hybrid differential games and establish the Max–Min Lemma for the two-player zero-sum game scenario. Next, we discuss the analysis of saddle-point equilibrium strategies for linear quadratic hybrid differential games, addressing both finite and infinite time horizons. Through the incorporation of a generalized Riccati differential equation (GRDE) and guided by the principles of the Itô–Liu formula, we prove that that solving the GRDE is crucial and serves as both a sufficient and necessary precondition for identifying equilibrium strategies within a finite horizon. In addition, we also acquire the explicit formulations of equilibrium strategies in closed forms, alongside determining the optimal values of the cost function. Through the adoption of a generalized Riccati equation (GRE) and applying a similar approach to that used for the finite horizon case, we establish that the ability to solve the GRE constitutes a sufficient criterion for the emergence of equilibrium strategies in scenarios extending over an infinite horizon. Moreover, we explore the dynamics of a resource extraction problem within a finite horizon and separately delve into an

H_{\infty}

control problem applicable to an infinite horizon. Finally, we present the conclusions. Full article

(This article belongs to the Special Issue Control Theory and Applications, 2nd Edition)

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16 pages, 2677 KiB

Open AccessArticle

Finite-Time Robust Path-Following Control of Perturbed Autonomous Ground Vehicles Using a Novel Self-Tuning Nonsingular Fast Terminal Sliding Manifold

by Cong Phat Vo, Quoc Hung Hoang, Tae-Hyun Kim and Jeong hwan Jeon

Mathematics 2024, 12(4), 549; https://doi.org/10.3390/math12040549 - 10 Feb 2024

Viewed by 2092

Abstract

This work presents a finite-time robust path-following control scheme for perturbed autonomous ground vehicles. Specifically, a novel self-tuning nonsingular fast-terminal sliding manifold that further enhances the convergence rate and tracking accuracy is proposed. Then, uncertain dynamics and external disturbances are estimated by a [...] Read more.

This work presents a finite-time robust path-following control scheme for perturbed autonomous ground vehicles. Specifically, a novel self-tuning nonsingular fast-terminal sliding manifold that further enhances the convergence rate and tracking accuracy is proposed. Then, uncertain dynamics and external disturbances are estimated by a high-gain disturbance observer to compensate for the designed control input. Successively, a super-twisting algorithm is incorporated into the final control law, significantly mitigating the chattering phenomenon of both the input control signal and the output trajectory. Furthermore, the global finite-time convergence and stability of the whole proposed control algorithm are proven by the Lyapunov theory. Finally, the efficacy of the proposed method is validated with comparisons in a numerical example. It obtains high control performance, reduced chattering, fast convergence rate, singularity avoidance, and robustness against uncertainties. Full article

(This article belongs to the Special Issue Control Theory and Applications, 2nd Edition)

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16 pages, 1794 KiB

Open AccessArticle

Stability Margin of Data-Driven LQR and Its Application to Consensus Problem

by Abdul Aris Umar, Kunhee Ryu, Juhoon Back and Jung-Su Kim

Mathematics 2024, 12(2), 199; https://doi.org/10.3390/math12020199 - 8 Jan 2024

Viewed by 1725

Abstract

In contrast with traditional control input design techniques based on mathematical models of the system, in data-driven control approaches, which have recently gained substantial attention, the controller is derived directly from the data that are collected from experiments or observations of the target [...] Read more.

In contrast with traditional control input design techniques based on mathematical models of the system, in data-driven control approaches, which have recently gained substantial attention, the controller is derived directly from the data that are collected from experiments or observations of the target system. In particular, several data-driven optimal control and model predictive control (MPC) techniques have been proposed. In this paper, it is shown that the recently proposed data-driven LQR (Linear Quadratic Regulator) has a stability margin that is the set of the uncertainties in the control input channels maintaining the closed-loop stability. As an application of the proposed stability margin of the data-driven LQR, the consensus problem is considered. Since the control design for the consensus of multi-agent systems can be reformulated into the robust stabilization of a linear system with uncertainty in the input channel, it is demonstrated that the derived stability margin can be used to design a controller for the consensus of multi-agent systems. Full article

(This article belongs to the Special Issue Control Theory and Applications, 2nd Edition)

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25 pages, 4011 KiB

Open AccessArticle

Predefined-Time Fractional-Order Tracking Control for UAVs with Perturbation

by Abdellah Benaddy, Moussa Labbadi, Sahbi Boubaker, Faisal S. Alsubaei and Mostafa Bouzi

Mathematics 2023, 11(24), 4886; https://doi.org/10.3390/math11244886 - 6 Dec 2023

Cited by 4 | Viewed by 1428

Abstract

This manuscript describes the design of a controller that assures predefined-time convergence in fractional-order sliding mode control (PTFOSMC) for a quadrotor UAV subjected to matched perturbation. Moreover, predefined-time techniques enable the establishment of a time constraint for convergence as a control parameter, distinguishing [...] Read more.

This manuscript describes the design of a controller that assures predefined-time convergence in fractional-order sliding mode control (PTFOSMC) for a quadrotor UAV subjected to matched perturbation. Moreover, predefined-time techniques enable the establishment of a time constraint for convergence as a control parameter, distinguishing them from finite- and fixed-time controllers. The proposed control offers the advantage of sliding mode control, exhibiting rapid response and robust performance for the quadrotor subsystems. Notably, the suggested controller is devoid of terms dependent on the initial conditions of the quadrotor. Additionally, an established switching-type predefined-time controller with fractional-order is introduced to bolster robustness against external disturbances and alleviate the chattering problem associated with the sliding mode technique. The application of the Lyapunov function is employed to analyze the predefined-time stability of the quadrotor utilizing the suggested PTFOSMC. Numerical results are provided to demonstrate the effectiveness of the suggested scheme. Full article

(This article belongs to the Special Issue Control Theory and Applications, 2nd Edition)

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Review

Jump to: Research

43 pages, 547 KiB

Open AccessReview

Complex Dynamics and Intelligent Control: Advances, Challenges, and Applications in Mining and Industrial Processes

by Luis Rojas, Víctor Yepes and José Garcia

Mathematics 2025, 13(6), 961; https://doi.org/10.3390/math13060961 - 14 Mar 2025

Cited by 1 | Viewed by 977

Abstract

Complex dynamics and nonlinear systems play a critical role in industrial processes, where complex interactions, high uncertainty, and external disturbances can significantly impact efficiency, stability, and safety. In sectors such as mining, manufacturing, and energy networks, even small perturbations can lead to unexpected [...] Read more.

Complex dynamics and nonlinear systems play a critical role in industrial processes, where complex interactions, high uncertainty, and external disturbances can significantly impact efficiency, stability, and safety. In sectors such as mining, manufacturing, and energy networks, even small perturbations can lead to unexpected system behaviors, operational inefficiencies, or cascading failures. Understanding and controlling these dynamics is essential for developing robust, adaptive, and resilient industrial systems. This study conducts a systematic literature review covering 2015–2025 in Scopus and Web of Science, initially retrieving 2628 (Scopus) and 343 (WoS) articles. After automated filtering (Python) and applying inclusion/exclusion criteria, a refined dataset of 2900 references was obtained, from which 89 highly relevant studies were selected. The literature was categorized into six key areas: (i) heat transfer with magnetized fluids, (ii) nonlinear control, (iii) big-data-driven optimization, (iv) energy transition via SOEC, (v) fault detection in control valves, and (vi) stochastic modeling with semi-Markov switching. Findings highlight the convergence of robust control, machine learning, IoT, and Industry 4.0 methodologies in tackling industrial challenges. Cybersecurity and sustainability also emerge as critical factors in developing resilient models, alongside barriers such as limited data availability, platform heterogeneity, and interoperability gaps. Future research should integrate multiscale analysis, deterministic chaos, and deep learning to enhance the adaptability, security, and efficiency of industrial operations in high-complexity environments. Full article

(This article belongs to the Special Issue Control Theory and Applications, 2nd Edition)

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