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Analysis and Mathematical Modeling of Control Engineering and Path Planning

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

Deadline for manuscript submissions: 31 May 2024 | Viewed by 15869

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Special Issue Editor

Dr. Sanda Florentina Mihalache

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Guest Editor

Automatic Control, Computers & Electronics Department, Petroleum-Gas University of Ploiești, 100680 Ploiești, Romania
Interests: cyberphysical systems; Industrial Internet of Things; Industry 4.0; resilience; cybersecurity of control systems; WSAN; numerical computing: numerical algorithms library of numerical methods, optimization algorithms; modeling and simulation of control systems for chemical processes; building knowledge bases, fuzzy rule bases, and models based on intelligent agents, decision support systems, machine learning, and fuzzy control systems; prediction and forecasting models for environmental pollution control

Special Issue Information

Dear Colleagues,

Mathematical modeling is a powerful tool in the context of the Industry 4.0 era. Migrating from industrial automation to industrial autonomy requires the development of a digital twin, a cyber representation for the physical system that must be controlled. Cyber representation is based on mathematical models that also comprise the real time behavior of the physical process along with its control structure. Industrial autonomy is also based on autonomous robots that must react to the changing environment and tasks according to path planning.

I am pleased to invite you to publish qualitative papers, referring but not limited to new and improved versions of existing mathematical models, designed at various observation and representation scales within an industrial control system, applicable in control engineering and path planning, along with their qualitative and quantitative analysis.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but not be limited to) the following: recent advances in mathematical modelling and inverse problems for industrial control systems, and mathematical modeling of path planning for industrial robots. Articles on real-time simulation, model order reduction, models based on artificial intelligence, and data-driven models are particularly welcome.

Please note that all of the submitted papers must be within the general scope of the Mathematics journal.

Dr. Sanda Florentina Mihalache
Guest Editor

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

dynamical systems
numerical methods
mathematical modeling
artificial intelligence methods
mathematical programming
identification and modeling of control systems
path planning algorithms

Published Papers (11 papers)

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Research

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20 pages, 5503 KiB

Open AccessArticle

Faster Implementation of The Dynamic Window Approach Based on Non-Discrete Path Representation

by Ziang Lin and Ryo Taguchi

Mathematics 2023, 11(21), 4424; https://doi.org/10.3390/math11214424 - 25 Oct 2023

Viewed by 1129

Abstract

The dynamic window approach (DWA) serves as a pivotal collision avoidance strategy for mobile robots, meticulously guiding a robot to its target while ensuring a safe distance from any perceivable obstacles in the vicinity. While the DWA has seen various enhancements and applications, its foundational computational process has predominantly remained constant, consequently resulting in a heightened level of time complexity. Inspired by the velocity invariance assumption inherent in the DWA and the utilization of polar coordinate transformations in the model, we introduce a high-speed version of the DWA. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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17 pages, 4607 KiB

Open AccessArticle

Enhancing Autonomous Guided Vehicles with Red-Black TOR Iterative Method

by A’Qilah Ahmad Dahalan, Azali Saudi and Jumat Sulaiman

Mathematics 2023, 11(20), 4393; https://doi.org/10.3390/math11204393 - 23 Oct 2023

Viewed by 711

Abstract

To address an autonomous guided vehicle problem, this article presents extended variants of the established block over-relaxation method known as the Block Modified Two-Parameter Over-relaxation (B-MTOR) method. The main challenge in handling autonomous-driven vehicles is to offer an efficient and reliable path-planning algorithm equipped with collision-free feature. This work intends to solve the path navigation with obstacle avoidance problem explicitly by using a numerical approach, where the mobile robot must project a route to outperform the efficiency of its travel from any initial position to the target location in the designated area. The solution builds on the potential field technique that uses Laplace’s equation to restrict the formation of potential functions across operating mobile robot regions. The existing block over-relaxation method and its variants evaluate the computation by obtaining four Laplacian potentials per computation in groups. These groups can also be viewed as groups of two points and single points if they’re close to the boundary. The proposed B-MTOR technique employs red-black ordering with four different weighted parameters. By carefully choosing the optimal parameter values, the suggested B-MTOR improved the computational execution of the algorithm. In red-black ordering, the computational molecules of red and black nodes are symmetrical. When the computation of red nodes is performed, the updated values of their four neighbouring black nodes are applied, and conversely. The performance of the newly proposed B-MTOR method is compared against the existing methods in terms of computational complexity and execution time. The simulation findings reveal that the red-black variants are superior to their corresponding regular variants, with the B-MTOR approach giving the best performance. The experiment also shows that, by applying a finite difference method, the mobile robot is capable of producing a collision-free path from any start to a given target point. In addition, the findings also verified that numerical techniques could provide an accelerated solution and have generated a smoother path than earlier work on the same issue. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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21 pages, 6308 KiB

Open AccessArticle

An Ensemble of Long Short-Term Memory Networks with an Attention Mechanism for Upper Limb Electromyography Signal Classification

by Naif D. Alotaibi, Hadi Jahanshahi, Qijia Yao, Jun Mou and Stelios Bekiros

Mathematics 2023, 11(18), 4004; https://doi.org/10.3390/math11184004 - 21 Sep 2023

Cited by 2 | Viewed by 964

Abstract

Advancing cutting-edge techniques to accurately classify electromyography (EMG) signals are of paramount importance given their extensive implications and uses. While recent studies in the literature present promising findings, a significant potential still exists for substantial enhancement. Motivated by this need, our current paper introduces a novel ensemble neural network approach for time series classification, specifically focusing on the classification of upper limb EMG signals. Our proposed technique integrates long short-term memory networks (LSTM) and attention mechanisms, leveraging their capabilities to achieve accurate classification. We provide a thorough explanation of the architecture and methodology, considering the unique characteristics and challenges posed by EMG signals. Furthermore, we outline the preprocessing steps employed to transform raw EMG signals into a suitable format for classification. To evaluate the effectiveness of our proposed technique, we compare its performance with a baseline LSTM classifier. The obtained numerical results demonstrate the superiority of our method. Remarkably, the method we propose attains an average accuracy of 91.5%, with all motion classifications surpassing the 90% threshold. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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17 pages, 2991 KiB

Open AccessArticle

Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-Beams

by Hajid Alsubaie, Amin Yousefpour, Ahmed Alotaibi, Naif D. Alotaibi and Hadi Jahanshahi

Mathematics 2023, 11(3), 789; https://doi.org/10.3390/math11030789 - 03 Feb 2023

Cited by 4 | Viewed by 1335

Abstract

This research investigates the stabilization and control of an uncertain Euler–Bernoulli nano-beam with fixed ends. The governing partial differential equations of motion for the nano-beam are derived using Hamilton’s principle and the non-local strain gradient theory. The Galerkin method is then applied to transform the resulting dimensionless partial differential equation into a nonlinear ordinary differential equation. A novel fault-tolerant terminal sliding mode control technique is proposed to address the uncertainties inherent in micro/nano-systems and the potential for faults and failures in control actuators. The proposed controller includes a finite time estimator, the stability of which and the convergence of the error dynamics are established using the Lyapunov theorem. The significance of this study lies in its application to the field of micro/nano-mechanics, where the precise control and stabilization of small-scale systems is crucial for the development of advanced technologies such as nano-robotics and micro-electromechanical systems (MEMS). The proposed control technique addresses the inherent uncertainties and potential for faults in these systems, making it a valuable choice for practical applications. The simulation results are presented to demonstrate the effectiveness of the proposed control scheme and the high accuracy of the estimation algorithm. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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25 pages, 2352 KiB

Open AccessArticle

A New Fuzzy Reinforcement Learning Method for Effective Chemotherapy

by Fawaz E. Alsaadi, Amirreza Yasami, Christos Volos, Stelios Bekiros and Hadi Jahanshahi

Mathematics 2023, 11(2), 477; https://doi.org/10.3390/math11020477 - 16 Jan 2023

Cited by 1 | Viewed by 1583

Abstract

A key challenge for drug dosing schedules is the ability to learn an optimal control policy even when there is a paucity of accurate information about the systems. Artificial intelligence has great potential for shaping a smart control policy for the dosage of drugs for any treatment. Motivated by this issue, in the present research paper a Caputo–Fabrizio fractional-order model of cancer chemotherapy treatment was elaborated and analyzed. A fix-point theorem and an iterative method were implemented to prove the existence and uniqueness of the solutions of the proposed model. Afterward, in order to control cancer through chemotherapy treatment, a fuzzy-reinforcement learning-based control method that uses the State-Action-Reward-State-Action (SARSA) algorithm was proposed. Finally, so as to assess the performance of the proposed control method, the simulations were conducted for young and elderly patients and for ten simulated patients with different parameters. Then, the results of the proposed control method were compared with Watkins’s Q-learning control method for cancer chemotherapy drug dosing. The results of the simulations demonstrate the superiority of the proposed control method in terms of mean squared error, mean variance of the error, and the mean squared of the control action—in other words, in terms of the eradication of tumor cells, keeping normal cells, and the amount of usage of the drug during chemotherapy treatment. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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19 pages, 742 KiB

Open AccessArticle

What Is the Best Way to Optimally Parameterize the MPC Cost Function for Vehicle Guidance?

by David Stenger, Robert Ritschel, Felix Krabbes, Rick Voßwinkel and Hendrik Richter

Mathematics 2023, 11(2), 465; https://doi.org/10.3390/math11020465 - 15 Jan 2023

Cited by 3 | Viewed by 1545

Abstract

Model predictive control (MPC) is a promising approach to the lateral and longitudinal control of autonomous vehicles. However, the parameterization of the MPC with respect to high-level requirements such as passenger comfort, as well as lateral and longitudinal tracking, is challenging. Numerous tuning parameters and conflicting requirements need to be considered. In this paper, we formulate the MPC tuning task as a multi-objective optimization problem. Its solution is demanding for two reasons: First, MPC-parameterizations are evaluated in a computationally expensive simulation environment. As a result, the optimization algorithm needs to be as sample-efficient as possible. Second, for some poor parameterizations, the simulation cannot be completed; therefore, useful objective function values are not available (for instance, learning with crash constraints). In this work, we compare the sample efficiency of multi-objective particle swarm optimization (MOPSO), a genetic algorithm (NSGA-II), and multiple versions of Bayesian optimization (BO). We extend BO by introducing an adaptive batch size to limit the computational overhead. In addition, we devise a method to deal with crash constraints. The results show that BO works best for a small budget, NSGA-II is best for medium budgets, and none of the evaluated optimizers are superior to random search for large budgets. Both proposed BO extensions are, therefore, shown to be beneficial. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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18 pages, 13878 KiB

Open AccessArticle

Control of a Hydraulic Generator Regulating System Using Chebyshev-Neural-Network-Based Non-Singular Fast Terminal Sliding Mode Method

by Fawaz E. Alsaadi, Amirreza Yasami, Hajid Alsubaie, Ahmed Alotaibi and Hadi Jahanshahi

Mathematics 2023, 11(1), 168; https://doi.org/10.3390/math11010168 - 29 Dec 2022

Cited by 7 | Viewed by 1386

Abstract

A hydraulic generator regulating system with electrical, mechanical, and hydraulic constitution is a complex nonlinear system, which is analyzed in this research. In the present study, the dynamical behavior of this system is investigated. Afterward, the input/output feedback linearization theory is exerted to derive the controllable model of the system. Then, the chaotic behavior of the system is controlled using a robust controller that uses a Chebyshev neural network as a disturbance observer in combination with a non-singular robust terminal sliding mode control method. Moreover, the convergence of the system response to the desired output in the presence of uncertainty and unexpected disturbances is demonstrated through the Lyapunov stability theorem. Finally, the effectiveness and appropriate performance of the proposed control scheme in terms of robustness against uncertainty and unexpected disturbances are demonstrated through numerical simulations. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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28 pages, 2019 KiB

Open AccessArticle

Dynamic Path Planning for the Differential Drive Mobile Robot Based on Online Metaheuristic Optimization

by Alejandro Rodríguez-Molina, Axel Herroz-Herrera, Mario Aldape-Pérez, Geovanni Flores-Caballero and Jarvin Alberto Antón-Vargas

Mathematics 2022, 10(21), 3990; https://doi.org/10.3390/math10213990 - 27 Oct 2022

Cited by 3 | Viewed by 2232

Abstract

Mobile robots are relevant dynamic systems in recent applications. Path planning is an essential task for these robots since it allows them to move from one location to another safely and at an affordable cost. Path planning has been studied extensively for static scenarios. However, when the scenarios are dynamic, research is limited due to the complexity and high cost of continuously re-planning the robot’s movements to ensure its safety. This paper proposes a new, simple, reliable, and affordable method to plan safe and optimized paths for differential mobile robots in dynamic scenarios. The method is based on the online re-optimization of the static parameters in the state-of-the-art deterministic path planner Bug0. Due to the complexity of the dynamic path planning problem, a metaheuristic optimization approach is adopted. This approach utilizes metaheuristics from evolutionary computation and swarm intelligence to find the Bug0 parameters when the mobile robot is approaching an obstacle. The proposal is tested in simulation, and well-known metaheuristic methods are compared, including Differential Evolution (DE), the Genetic Algorithm (GA), and Particle Swarm Optimization (PSO). The dynamic planner based on PSO generates paths with the best performances. In addition, the results of the PSO-based planner are compared with different Bug0 configurations, and the former is shown to be significantly better. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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12 pages, 7553 KiB

Open AccessArticle

Collision Avoidance Problem of Ellipsoid Motion

by Shujun Guo, Lujing Jing, Zhaopeng Dai, Yang Yu, Zhiqing Dang, Zhihang You, Ang Su, Hongwei Gao, Jinqiu Guan and Yujun Song

Mathematics 2022, 10(19), 3478; https://doi.org/10.3390/math10193478 - 23 Sep 2022

Viewed by 909

Abstract

This paper studies the problem of target control and how a virtual ellipsoid can avoid the static obstacle. During the motion to the target set, the virtual ellipsoid can achieve a motion under collision avoidance by keeping the distance between the ellipsoid and obstacle. We present solutions to this problem in the class of closed-loop (feedback) controls based on Hamilton–Jacobi–Bellman (HJB) equation. Simulation results verify the validity and effectiveness of our algorithm. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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18 pages, 5427 KiB

Open AccessArticle

Indirect Neural-Enhanced Integral Sliding Mode Control for Finite-Time Fault-Tolerant Attitude Tracking of Spacecraft

by Qijia Yao, Hadi Jahanshahi, Stelios Bekiros, Sanda Florentina Mihalache and Naif D. Alotaibi

Mathematics 2022, 10(14), 2467; https://doi.org/10.3390/math10142467 - 15 Jul 2022

Cited by 14 | Viewed by 1372

Abstract

In this article, a neural integral sliding mode control strategy is presented for the finite-time fault-tolerant attitude tracking of rigid spacecraft subject to unknown inertia and disturbances. First, an integral sliding mode controller was developed by originally constructing a novel integral sliding mode surface to avoid the singularity problem. Then, the neural network (NN) was embedded into the integral sliding mode controller to compensate the lumped uncertainty and replace the robust switching term. In this way, the chattering phenomenon was significantly suppressed. Particularly, the mechanism of indirect neural approximation was introduced through inequality relaxation. Benefiting from this design, only a single learning parameter was required to be adjusted online, and the computation burden of the proposed controller was extremely reduced. The stability argument showed that the proposed controller could guarantee that the attitude and angular velocity tracking errors were regulated to the minor residual sets around zero in a finite time. It was noteworthy that the proposed controller was not only strongly robust against unknown inertia and disturbances, but also highly insensitive to actuator faults. Finally, the effectiveness and advantages of the proposed control strategy were validated using simulations and comparisons. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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Review

Jump to: Research

19 pages, 595 KiB

Open AccessReview

Towards Sustainable Transportation: A Review of Fuzzy Decision Systems and Supply Chain Serviceability

by Hadi Jahanshahi, Zahra Alijani and Sanda Florentina Mihalache

Mathematics 2023, 11(8), 1934; https://doi.org/10.3390/math11081934 - 20 Apr 2023

Cited by 3 | Viewed by 1275

Abstract

Modern requirements dictate the need for sustainable transportation systems, given the substantial growth in transportation activities over recent years that is predicted to persist. This surge in transportation has brought about environmental concerns such as air pollution and noise. To deal with this crisis, municipal administrations are investing in sustainable, reliable, economical, and environmentally friendly transportation systems. This review examines the latest developments in fuzzy decision systems for sustainable transport supplements. By reviewing the literature, we assess the serviceability of the entire supply chain to maintain transport quality, remove degradation, and meet customer demands. The link between fuzzy decision systems and supply chain serviceability may not be immediately obvious, but there are many reasons why putting them together can be a valuable focus for companies. By leveraging the capabilities of fuzzy decision systems to optimize supply chain processes and improve service levels, companies can gain a competitive advantage and better meet customer demand. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Control Engineering and Path Planning)

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