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Advanced Control Theory with Applications
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Advanced Control Theory with Applications

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

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 28334

Special Issue Editors

Prof. Dr. Fang Liu

E-Mail Website
Guest Editor
School of Automation, Central South University, Changsha 410083, China
Interests: smart grid; time-delay systems; deep learning; advanced control algorithm
Special Issues, Collections and Topics in MDPI journals
Dr. Qianyi Liu

E-Mail Website
Guest Editor
School of Automation, Central South University, Changsha 410083, China
Interests: electrical energy optimization; renewable power generation; industrial supply system

Special Issue Information

Dear Colleagues,

Control theory with application pertains to the study of control and decision technology and its application in complex, dynamic and interconnected systems. Control theory with application has witnessed dramatic achievements, which play a central role in most applications, such as smart grids, power systems, aerospace, robotics, intelligent transportation systems, etc. The establishment of mathematical models and the design of control methods are particularly important. The aim of this Special Issue is to explore and disseminate the latest research and development in the application of control theory and control technology to industrial production. We are looking for original papers with novel research contributions in all aspects of control theory that have relevance and impactful applications. Topics of interest include, but are not limited to:

  • Methods of networked control systems;
  • Methods of time-delay control systems;
  • Multi-agent control system;
  • Application of artificial intelligence technology in control theory;
  • Methods of analysis and synthesis of control modes;
  • Methods of numerical simulation for control systems;
  • Complex problems of intelligent modeling and control systems;
  • Application of advanced control theory in smart grid;
  • Operation and optimization of power system.

High-quality research and surveys reflecting the current state of affairs are welcome. Particular attention should be paid to the practical application of research results.

Prof. Dr. Fang Liu
Dr. Qianyi Liu
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

  • time-delay systems
  • networked control systems
  • multi-agent
  • artificial intelligence methods
  • intelligent modeling
  • iIntelligent control
  • smart industrial
  • smart grid
  • optimization

Published Papers (20 papers)

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Research

18 pages, 1067 KiB  
Article
A Finite-Time Sliding Mode Control Approach for Constrained Euler–Lagrange System
by Guhao Sun and Qingshuang Zeng
Mathematics 2023, 11(12), 2788; https://doi.org/10.3390/math11122788 - 20 Jun 2023
Viewed by 1022
Abstract
This paper investigates a general control strategy to track the reference trajectory for the constrained Euler–Lagrange system with model uncertainties and unknown external disturbances. Unlike the disturbances assumed to be upper-bounded by a constant in other papers, we consider the disturbances to be [...] Read more.
This paper investigates a general control strategy to track the reference trajectory for the constrained Euler–Lagrange system with model uncertainties and unknown external disturbances. Unlike the disturbances assumed to be upper-bounded by a constant in other papers, we consider the disturbances to be bounded by a function of the system states, which are more realistic. First, the nominal controller was designed based on the nonsingular fast terminal sliding mode control, and global fast finite-time convergence to the sliding surface was guaranteed. As the system is state-constrained in this paper, we introduce the control barrier function approach to formulate the constraints and ensure the system does not break the restrictions. The proposed control strategy was numerically assessed on a two-link robot manipulator system, and the simulation results illustrate the effectiveness of the proposed control strategy. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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17 pages, 998 KiB  
Article
LCANet: A Lightweight Context-Aware Network for Bladder Tumor Segmentation in MRI Images
by Yixing Wang, Xiang Li and Xiufen Ye
Mathematics 2023, 11(10), 2357; https://doi.org/10.3390/math11102357 - 18 May 2023
Cited by 1 | Viewed by 1442
Abstract
Accurate segmentation of the lesion area from MRI images is essential for diagnosing bladder cancer. However, the precise segmentation of bladder tumors remains a massive challenge due to their similar intensity distributions, various tumor morphologies, and blurred boundaries. While some seminal studies, such [...] Read more.
Accurate segmentation of the lesion area from MRI images is essential for diagnosing bladder cancer. However, the precise segmentation of bladder tumors remains a massive challenge due to their similar intensity distributions, various tumor morphologies, and blurred boundaries. While some seminal studies, such as those using CNNs combined with transformer segmentation methods, have made significant progress, (1) how to reduce the computational complexity of the self-attention mechanism in the transformer while maintaining performance and (2) how to build a better global feature fusion process to improve segmentation performance still require further exploration. Considering the complexity of bladder MRI images, we developed a lightweight context-aware network (LCANet) to automatically segment bladder lesions from MRI images. Specifically, the local detail encoder generates local-level details of the lesion, the lightweight transformer encoder models the global-level features with different resolutions, the pyramid scene parsing module extracts high-level and multiscale semantic features, and the decoder provides high-resolution segmentation results by fusing local-level details with global-level cues at the channel level. A series of empirical studies on T2-weighted MRI images from 86 patients show that LCANet achieves an overall Jaccard index of 89.39%, a Dice similarity coefficient of 94.08%, and a Class pixel accuracy of 94.10%. These advantages show that our method is an efficient tool that can assist in reducing the heavy workload of radiologists. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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16 pages, 4185 KiB  
Article
Dynamic Event-Triggered Consensus Control for Markovian Switched Multi-Agent Systems: A Hybrid Neuroadaptive Method
by Xue Luo, Jingyi Wang, Jianwen Feng, Jiayi Cai and Yi Zhao
Mathematics 2023, 11(9), 2196; https://doi.org/10.3390/math11092196 - 6 May 2023
Cited by 2 | Viewed by 1220
Abstract
This paper presents a solution to the consensus problem for a particular category of uncertain switched multi-agent systems (MASs). In these systems, the communication topologies between agents and the system dynamics are governed by a time-homogeneous Markovian chain in a stochastic manner. To [...] Read more.
This paper presents a solution to the consensus problem for a particular category of uncertain switched multi-agent systems (MASs). In these systems, the communication topologies between agents and the system dynamics are governed by a time-homogeneous Markovian chain in a stochastic manner. To address this issue, we propose a novel neuroadaptive distributed dynamic event-triggered control (DETC) strategy. By leveraging stochastic Lyapunov theory and matrix inequality methodology, we establish sufficient conditions for practical ultimate mean square consensus (UMSBC) of MASs using a combination of neural networks (NNs) adaptive control strategy and DETC method. Our approach employs a distributed adaptive NNs DETC mechanism in MASs with unknown nonlinear dynamics and upgrades it at the moment of event sampling in an aperiodic manner, resulting in significant savings in computation and resources. We also exclude the Zeno phenomenon. Finally, we provide numerical examples to demonstrate the feasibility of our proposed approach, which outperforms existing approaches. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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21 pages, 1671 KiB  
Article
Maximum Power Point Tracker Controller for Solar Photovoltaic Based on Reinforcement Learning Agent with a Digital Twin
by Eneko Artetxe, Jokin Uralde, Oscar Barambones, Isidro Calvo and Imanol Martin
Mathematics 2023, 11(9), 2166; https://doi.org/10.3390/math11092166 - 5 May 2023
Cited by 2 | Viewed by 1738
Abstract
Photovoltaic (PV) energy, representing a renewable source of energy, plays a key role in the reduction of greenhouse gas emissions and the achievement of a sustainable mix of energy generation. To achieve the maximum solar energy harvest, PV power systems require the implementation [...] Read more.
Photovoltaic (PV) energy, representing a renewable source of energy, plays a key role in the reduction of greenhouse gas emissions and the achievement of a sustainable mix of energy generation. To achieve the maximum solar energy harvest, PV power systems require the implementation of Maximum Power Point Tracking (MPPT). Traditional MPPT controllers, such as P&O, are easy to implement, but they are by nature slow and oscillate around the MPP losing efficiency. This work presents a Reinforcement learning (RL)-based control to increase the speed and the efficiency of the controller. Deep Deterministic Policy Gradient (DDPG), the selected RL algorithm, works with continuous actions and space state to achieve a stable output at MPP. A Digital Twin (DT) enables simulation training, which accelerates the process and allows it to operate independent of weather conditions. In addition, we use the maximum power achieved in the DT to adjust the reward function, making the training more efficient. The RL control is compared with a traditional P&O controller to validate the speed and efficiency increase both in simulations and real implementations. The results show an improvement of 10.45% in total power output and a settling time 24.54 times faster in simulations. Moreover, in real-time tests, an improvement of 51.45% in total power output and a 0.25 s settling time of the DDPG compared with 4.26 s of the P&O is obtained. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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13 pages, 1356 KiB  
Article
Design of Distributed Interval Observers for Multiple Euler–Lagrange Systems
by Zhihang Yin, Jun Huang and Thach Ngoc Dinh
Mathematics 2023, 11(8), 1872; https://doi.org/10.3390/math11081872 - 14 Apr 2023
Cited by 1 | Viewed by 1154
Abstract
This paper investigates the problem of distributed interval estimation for multiple Euler–Lagrange systems. An interconnection topology is supposed to be strongly connected. To design distributed interval observers, the coordinate transformation method is employed. The construction of the distributed interval observer is given by [...] Read more.
This paper investigates the problem of distributed interval estimation for multiple Euler–Lagrange systems. An interconnection topology is supposed to be strongly connected. To design distributed interval observers, the coordinate transformation method is employed. The construction of the distributed interval observer is given by the monotone system theory, and the stability is analyzed by the Lyapunov stability theory. Unlike the current works, each sub-interval observer has its own gain; in addition to this, additional observer gains are used to reduce the conservatism of design. The gains of all sub-interval observers are determined by both the monotone system theory and the Lyapunov stability theory. Finally, a simulation example verifies the feasibility of the presented distributed interval observers. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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32 pages, 10027 KiB  
Article
Development of Slime Mold Optimizer with Application for Tuning Cascaded PD-PI Controller to Enhance Frequency Stability in Power Systems
by Slim Abid, Ali M. El-Rifaie, Mostafa Elshahed, Ahmed R. Ginidi, Abdullah M. Shaheen, Ghareeb Moustafa and Mohamed A. Tolba
Mathematics 2023, 11(8), 1796; https://doi.org/10.3390/math11081796 - 10 Apr 2023
Cited by 15 | Viewed by 1505
Abstract
Multi-area power systems (MAPSs) are highly complex non-linear systems facing a fundamental issue in real-world engineering problems called frequency stability problems (FSP). This paper develops an enhanced slime mold optimization algorithm (ESMOA) to optimize the tuning parameters for a cascaded proportional derivative-proportional integral [...] Read more.
Multi-area power systems (MAPSs) are highly complex non-linear systems facing a fundamental issue in real-world engineering problems called frequency stability problems (FSP). This paper develops an enhanced slime mold optimization algorithm (ESMOA) to optimize the tuning parameters for a cascaded proportional derivative-proportional integral (PD-PI) controller. The novel ESMOA proposal includes a new system that combines basic SMO, chaotic dynamics, and an elite group. The motion update incorporates the chaotic technique, and the exploitation procedure is enhanced by searching for a select group rather than merely the best solution overall. The proposed cascaded PD-PI controller based on the ESMOA is employed for solving the FSP in MAPSs with two area non-reheat thermal systems to keep the balance between the electrical power load and the generation and provide power system security, reliability, and quality. The proposed cascaded PD-PI controller based on the ESMOA is evaluated using time domain simulation to minimize the integral time-multiplied absolute error (ITAE). It is evaluated in four different test situations with various sets of perturbations. For tuning the cascaded PD-PI controller, the proposed ESMOA is compared to the golden search optimizer (GSO) and circle optimizer (CO), where the proposed ESMOA provides the best performance. Furthermore, the findings of the proposed cascaded PD-PI controller based on the ESMOA outperform previous published PID and PI controllers adjusted using numerous contemporary techniques. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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15 pages, 3505 KiB  
Article
Motion Synchronization Control for a Large Civil Aircraft’s Hybrid Actuation System Using Fuzzy Logic-Based Control Techniques
by Waheed Ur Rehman, Xingjian Wang, Zeeshan Hameed and Muhammad Yasir Gul
Mathematics 2023, 11(7), 1576; https://doi.org/10.3390/math11071576 - 24 Mar 2023
Cited by 2 | Viewed by 1233
Abstract
The motion synchronization of the hybrid actuation system (composed of a servo-hydraulic actuator and an electro-mechanical actuator) is very important for all applications, especially for civil aircraft. The current research presents a nested-loop control design technique to synchronize motion between two different actuators, [...] Read more.
The motion synchronization of the hybrid actuation system (composed of a servo-hydraulic actuator and an electro-mechanical actuator) is very important for all applications, especially for civil aircraft. The current research presents a nested-loop control design technique to synchronize motion between two different actuators, such as a servo-hydraulic actuator (SHA) and an electro-mechanical actuator (EMA). The proposed strategy consists of a trajectory, an intelligent position controller (fuzzy logic-based controller), a feed-forward controller, and an intelligent force controller (fuzzy logic-based controller). Position, speed, and acceleration signals are produced by trajectory at a frequency that both SHA and EMA can follow. The SHA/EMA system’s position tracking performance is enhanced by the feed-forward controller and intelligent position controller working together, while the intelligent force tracking controller lowers the issue of force fighting by focusing on the rigid coupling effect. To verify the effectiveness of the proposed strategy, simulations are performed in the Matlab/Simulink environment. The result shows that the proposed intelligent control strategy not only reduces initial force fighting, but also improves load-rejection performance and output-trajectory tracking performance. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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24 pages, 6963 KiB  
Article
A Novel Adaptive Finite-Time Position Tracking Control Strategy for Teleoperation System with Varying Communication Delays
by Haochen Zhang, Liyue Fu and Ancai Zhang
Mathematics 2023, 11(6), 1486; https://doi.org/10.3390/math11061486 - 18 Mar 2023
Cited by 1 | Viewed by 1085
Abstract
Based on the traditional control approach, the position-tracking performance of the teleoperation system with communication delay is generally asymptotically stable. In practical applications, the closed-loop system is expected to achieve stable and finite-time convergence performance. A novel finite-time bilateral control scheme for a [...] Read more.
Based on the traditional control approach, the position-tracking performance of the teleoperation system with communication delay is generally asymptotically stable. In practical applications, the closed-loop system is expected to achieve stable and finite-time convergence performance. A novel finite-time bilateral control scheme for a telerobotics system with communication delay is presented in this paper. On the basis of the traditional proportional damping injection control, this paper proposes and designs a new finite-time control method by introducing the non-integer power to the position error, velocity, and the combined error with position error and velocity. In comparison to existing proportional damping injection and finite-time control structures, the proposed method not only achieves the finite-time convergence performance of position tracking, but it also has the advantages of a simple structure and fewer gain coefficients. The controller also incorporates the radial basis function (RBF) neural network and adaptive approach to compensate unknown dynamics and external forces, thus also avoiding the measurement of force signals. The Lyapunov–Krasovskii function is then defined, and it is demonstrated that the position tracking of closed-loop teleoperation system has bounded stability and finite-time control performance. The simulation experiment is also performed, and the results further illustrated the bounded stability of the system. Moreover, compared to the position tracking errors of other non-finite-time control methods, it is demonstrated that the proposed finite-time control scheme has a faster convergence rate and higher convergence precision. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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20 pages, 3305 KiB  
Article
A Method of Optimizing Cell Voltage Based on STA-LSSVM Model
by Chenhua Xu, Zhicheng Tu, Wenjie Zhang, Jian Cen, Jianbin Xiong and Na Wang
Mathematics 2022, 10(24), 4710; https://doi.org/10.3390/math10244710 - 12 Dec 2022
Cited by 3 | Viewed by 1139
Abstract
It is challenging to control and optimize the aluminum electrolysis process due to its non-linearity and high energy consumption. Reducing the cell voltage is crucial for energy consumption reduction. This paper presents an intelligent method of predicting and optimizing cell voltage based on [...] Read more.
It is challenging to control and optimize the aluminum electrolysis process due to its non-linearity and high energy consumption. Reducing the cell voltage is crucial for energy consumption reduction. This paper presents an intelligent method of predicting and optimizing cell voltage based on the evaluation of modeling the comprehensive cell state. Firstly, the Savitzky–Golay filtering algorithm(SGFA) is adopted to denoise the sample data to improve the accuracy of the experimental model. Due to the influencing factors of the cell state, a comprehensive evaluation model of the cell state is established. Secondly, the model of the least squares supports vector machine (LSSVM) is proposed to predict the cell voltage. In order to improve the accuracy of the model, the state transition algorithm (STA) is employed to optimize the structure parameters of the model. Thirdly, the optimization and control model of the cell voltage is developed by an analysis of the technical conditions. Then, the STA is used to realize the optimization of the front model. Finally, the actual data were applied to the experiments of the above method, and the proposed STA was compared with other methods. The results of experiments show that this method is efficient and satisfactory. The optimization value of average cell voltage based on the STA-LSSVM is 3.8165v, and it can be used to guide process operation. The DC power consumption is 11,971 KW·h per tonne of aluminum, with a reduction in power consumption of 373 KW·h. This result guarantees the reduction of aluminum electrolysis energy consumption. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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21 pages, 8461 KiB  
Article
An Adaptive Proportional Plus Damping Control for Teleoperation Systems with Asymmetric Time-Varying Communication Delays
by Jigang Bao, Liyue Fu, Haochen Zhang, Ancai Zhang, Wenhui Guo and Tiansheng Chen
Mathematics 2022, 10(24), 4675; https://doi.org/10.3390/math10244675 - 9 Dec 2022
Cited by 2 | Viewed by 828
Abstract
Communication delay is an important factor affecting the stability and performance of telerobotic systems. In this paper, a new adaptive proportional damping controller is proposed to improve the stability and performance of the system in the presence of the cases such as asymmetric [...] Read more.
Communication delay is an important factor affecting the stability and performance of telerobotic systems. In this paper, a new adaptive proportional damping controller is proposed to improve the stability and performance of the system in the presence of the cases such as asymmetric communication delay, unknown gravity torque, friction torque, and other disturbance torques. The proposed proportional damping control method combines the RBF neural network and adaptive control strategy to compensate for the unknown torque. The stability and robustness of the system are enhanced by adding error-damping items, operator force, and environmental force items. The Lyapunov–Krasovskii functional is employed to analyze and prove the exponential stability and signal boundedness of the closed-loop system. The simulation results verify the correctness of the proposed method, and the comparison with the results of other control methods shows the effectiveness of the designed control strategy. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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13 pages, 1327 KiB  
Article
New Delay-Partitioning LK-Functional for Stability Analysis with Neutral Type Systems
by Liming Ding, Liqin Chen, Dajiang He and Weiwei Xiang
Mathematics 2022, 10(21), 4119; https://doi.org/10.3390/math10214119 - 4 Nov 2022
Viewed by 1028
Abstract
This paper investigates the stability issues associated with neutral-type delay systems. Firstly, the delay-partitioning method is employed to construct a brand-new LK-functional candidate. The discrete delay and a neutral delay are divided into several piecewise points through a relaxable sequence of constant numbers, [...] Read more.
This paper investigates the stability issues associated with neutral-type delay systems. Firstly, the delay-partitioning method is employed to construct a brand-new LK-functional candidate. The discrete delay and a neutral delay are divided into several piecewise points through a relaxable sequence of constant numbers, are increasing at a steady rate and are not larger than 1. Secondly, to fully use the interconnection information among the delayed state vectors, a new LK-functional is constructed. Thirdly, the recently published single/multiple integral inequalities are employed to bound the derivative of the newly developed LK function. Finally, a novel stability criterion for neutral systems is developed based on the above treatment. Furthermore, a new corollary is also proposed for the condition of τ=h. The benefits and productivities of our method are demonstrated by numerical examples. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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11 pages, 744 KiB  
Article
Exponential Synchronization of Hyperbolic Complex Spatio-Temporal Networks with Multi-Weights
by Hongkun Ma and Chengdong Yang
Mathematics 2022, 10(14), 2451; https://doi.org/10.3390/math10142451 - 14 Jul 2022
Cited by 4 | Viewed by 1092
Abstract
This paper deals with the leader-following synchronization of first-order, semi-linear, complex spatio-temporal networks. Firstly, two sorts of complex spatio-temporal networks based on hyperbolic partial differential equations (CSTNHPDEs) are built: one with a single weight and the other with multi-weights. Then, a new distributed [...] Read more.
This paper deals with the leader-following synchronization of first-order, semi-linear, complex spatio-temporal networks. Firstly, two sorts of complex spatio-temporal networks based on hyperbolic partial differential equations (CSTNHPDEs) are built: one with a single weight and the other with multi-weights. Then, a new distributed controller is designed to address CSTNHPDE with a single weight. Sufficient conditions for the synchronization and exponential synchronization of CSTNHPDE are presented by showing the gain ranges. Thirdly, the proposed distributed controller addresses of CSTNHPDE with multi-weights, and gain ranges are obtained for synchronization and exponential synchronization, respectively. Finally, two examples show the effectiveness and good performance of the control methods. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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11 pages, 526 KiB  
Article
A Novel MRAC Scheme for Output Tracking
by Tingting Tian, Xiaorong Hou and Fang Yan
Mathematics 2022, 10(14), 2384; https://doi.org/10.3390/math10142384 - 7 Jul 2022
Viewed by 1131
Abstract
This paper puts forward a novel output feedback model reference adaptive control (MRAC) scheme for solving an adaptive output tracking problem. The proposed control scheme only needs a scalar function to be updated online, which decreases the system adaptation complexity, compared to the [...] Read more.
This paper puts forward a novel output feedback model reference adaptive control (MRAC) scheme for solving an adaptive output tracking problem. The proposed control scheme only needs a scalar function to be updated online, which decreases the system adaptation complexity, compared to the existing MRAC schemes. Furthermore, the closed-loop signal boundedness and asymptotic output tracking are guaranteed with the proposed MRAC scheme. A simulation study is carried out to verify the effectiveness of the established approach. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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9 pages, 2211 KiB  
Article
Stabilization Control of Underactuated Spring-Coupled Three-Link Horizontal Manipulator Based on Energy Absorption Idea
by Ancai Zhang, Lu Fan, Shuli Gong, Guangyuan Pan and Yinghua Wu
Mathematics 2022, 10(11), 1832; https://doi.org/10.3390/math10111832 - 26 May 2022
Viewed by 1182
Abstract
A spring-coupled three-link horizontal manipulator (STHM) is an underactuated mechanical system that possesses two control inputs and three degrees of freedom (DOF). This paper discusses the stabilization control problem for this multi-DOF underactuated system. By using an energy-absorbing idea, we design two types [...] Read more.
A spring-coupled three-link horizontal manipulator (STHM) is an underactuated mechanical system that possesses two control inputs and three degrees of freedom (DOF). This paper discusses the stabilization control problem for this multi-DOF underactuated system. By using an energy-absorbing idea, we design two types of virtual friction controllers: PsD controller and PD controller. Additionally, the stability of the control system is analyzed based on Lyapunov theory and LaSalle’s invariance principle. The design of the stabilizing controller in this paper makes good use of the physical characteristics of the STHM system. The design process of the whole control system is simple. Numerical examples demonstrate the validity and superiority of our developed control strategy. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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20 pages, 9941 KiB  
Article
Design of an NSMCR Based Controller for All-Electric Aircraft Anti-Skid Braking System
by Xuelin Liang, Fengrui Xu, Mengqiao Chen and Wensheng Liu
Mathematics 2022, 10(10), 1715; https://doi.org/10.3390/math10101715 - 17 May 2022
Viewed by 1840
Abstract
In this paper, a relative threshold event-triggered based novel complementary sliding mode control (NSMCR) algorithm of all-electric aircraft (AEA) anti-skid braking system (ABS) is proposed to guarantee the braking stability and tracking precision of reference wheel slip control. First, a model of the [...] Read more.
In this paper, a relative threshold event-triggered based novel complementary sliding mode control (NSMCR) algorithm of all-electric aircraft (AEA) anti-skid braking system (ABS) is proposed to guarantee the braking stability and tracking precision of reference wheel slip control. First, a model of the braking system is established in strict-feedback form. Then a virtual controller with a nonlinear control algorithm is proposed to address the problem of constraint control regarding wheel slip rate with asymptotical stability. Next, a novel approaching law-based complementary sliding mode controller is developed to keep track of braking pressure. Moreover, the robust adaptive law is designed to estimate the uncertainties of the braking systems online to alleviate the chattering problem of the braking pressure controller. Additionally, to reduce the network communication and actuator wear of AEA-ABS, a relative threshold event trigger mechanism is proposed to transmit the output of NSMC in demand. The simulation results under various algorithms regarding three types of runway indicate that the proposed algorithms can improve the performance of braking control. In addition, the hardware-in-the-loop (HIL) experimental results prove that the proposed methods are practical for real-time applications. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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23 pages, 379 KiB  
Article
On the Stabilization through Linear Output Feedback of a Class of Linear Hybrid Time-Varying Systems with Coupled Continuous/Discrete and Delayed Dynamics with Eventually Unbounded Delay
by Manuel De la Sen
Mathematics 2022, 10(9), 1424; https://doi.org/10.3390/math10091424 - 23 Apr 2022
Viewed by 1065
Abstract
This research studies a class of linear, hybrid, time-varying, continuous time-systems with time-varying delayed dynamics and non-necessarily bounded, time-varying, time-differentiable delay. The considered class of systems also involves a contribution to the whole delayed dynamics with respect to the last preceding sampled values [...] Read more.
This research studies a class of linear, hybrid, time-varying, continuous time-systems with time-varying delayed dynamics and non-necessarily bounded, time-varying, time-differentiable delay. The considered class of systems also involves a contribution to the whole delayed dynamics with respect to the last preceding sampled values of the solution according to a prefixed constant sampling period. Such systems are also subject to linear output-feedback time-varying control, which picks-up combined information on the output at the current time instant, the delayed one, and its discretized value at the preceding sampling instant. Closed-loop asymptotic stabilization is addressed through the analysis of two “ad hoc” Krasovskii–Lyapunov-type functional candidates, which involve quadratic forms of the state solution at the current time instant together with an integral-type contribution of the state solution along a time-varying previous time interval associated with the time-varying delay. An analytic method is proposed to synthesize the stabilizing output-feedback time-varying controller from the solution of an associated algebraic system, which has the objective of tracking prescribed suited reference closed-loop dynamics. If this is not possible—in the event that the mentioned algebraic system is not compatible—then a best approximation of such targeted closed-loop dynamics is made in an error-norm sense minimization. Sufficiency-type conditions for asymptotic stability of the closed-loop system are also derived based on the two mentioned Krasovskii–Lyapunov functional candidates, which involve evaluations of the contributions of the delay-free and delayed dynamics. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
14 pages, 21042 KiB  
Article
Synthesized Landing Strategy for Quadcopter to Land Precisely on a Vertically Moving Apron
by Nguyen Xuan Mung, Ngoc Phi Nguyen, Dinh Ba Pham, Nhu Ngoc Dao and Sung Kyung Hong
Mathematics 2022, 10(8), 1328; https://doi.org/10.3390/math10081328 - 17 Apr 2022
Cited by 11 | Viewed by 1971
Abstract
Quadcopter unmanned aerial vehicles have become increasingly popular for various real-world applications, and a significant body of literature exists regarding the improvement of their flight capabilities to render them fully autonomous. The precise landing onto moving platforms, such as ship decks, is one [...] Read more.
Quadcopter unmanned aerial vehicles have become increasingly popular for various real-world applications, and a significant body of literature exists regarding the improvement of their flight capabilities to render them fully autonomous. The precise landing onto moving platforms, such as ship decks, is one of the remaining challenges that is largely unresolved. The reason why this operation poses a considerable challenge is because landing performance is considerably degraded by the ground effect or external disturbances. In this paper, we propose a synthesized landing algorithm that allows a quadcopter to land precisely on a vertically moving pad. Firstly, we introduce a disturbance observer-based altitude controller that allows the vehicle to perform robust altitude flight in the presence of external disturbances and the ground effect, strictly proving the system’s stability using Lyapunov’s theory. Secondly, we derive an apron state estimator to provide information on the landing target’s relative position. Additionally, we propose a landing planner to ensure that the landing task is completed in a safe and reliable manner. Finally, the proposed algorithms are implemented in an actual quadcopter, and we demonstrate the effectiveness and applicability of our method through real flight experiments. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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18 pages, 5540 KiB  
Article
A Generalized Construction Model for CT Projection-Wise Filters on the SDBP Technique
by Yiming Jiang, Jintao Zhao, Xiaodong Hu and Jing Zou
Mathematics 2022, 10(4), 579; https://doi.org/10.3390/math10040579 - 13 Feb 2022
Viewed by 1333
Abstract
Nowadays, with the rapid development of computed tomography (CT), the theoretical expansion of CT reconstruction has become the crucial ingredient to break through technical bottlenecks. This article supplements relevant knowledge of the method for constructing CT projection-wise filters. From the perspective of the [...] Read more.
Nowadays, with the rapid development of computed tomography (CT), the theoretical expansion of CT reconstruction has become the crucial ingredient to break through technical bottlenecks. This article supplements relevant knowledge of the method for constructing CT projection-wise filters. From the perspective of the mathematical principle of CT reconstruction, the second-order divided-difference back projection (SDBP) technique is firstly proposed, which is an implementation of accurate and efficient inverse Radon transform. On the basis of the SDBP technique, a brand new computational model for filter expressions is derived. The model reveals the correlation between the convolution kernel for data restoration and the filter expression and also specifies the principle of filter construction. On the proposed filter construction model, the decomposition form of filters is discovered for the first time. A series of basic filters are acquired, which can be used to compose filters in actual need. According to the superposition principle, the properties of a filter depend on the decomposed basic filters. The selection of the kernel function on the properties of basic filters clarifies the general rule of filter construction. These theories proposed in this article are of reference value for the filter optimization research in the CT reconstruction field. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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15 pages, 1150 KiB  
Article
Synchronization of Nonlinear Complex Spatiotemporal Networks Based on PIDEs with Multiple Time Delays: A P-sD Method
by Jiashu Dai and Chengdong Yang
Mathematics 2022, 10(3), 509; https://doi.org/10.3390/math10030509 - 5 Feb 2022
Cited by 3 | Viewed by 1243
Abstract
This paper studies the synchronization control of nonlinear multiple time-delayed complex spatiotemporal networks (MTDCSNs) based on partial integro-differential equations. Firstly, dealing with an MTDCSN with time-invariant delays, P-sD control is employed and the synchronization criteria are obtained in terms of LMIs. Secondly, this [...] Read more.
This paper studies the synchronization control of nonlinear multiple time-delayed complex spatiotemporal networks (MTDCSNs) based on partial integro-differential equations. Firstly, dealing with an MTDCSN with time-invariant delays, P-sD control is employed and the synchronization criteria are obtained in terms of LMIs. Secondly, this control method is further used in an MTDCSN with time-varying delays. An example illustrates the effectiveness of the proposed methods. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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14 pages, 698 KiB  
Article
Consensus Control of Leaderless and Leader-Following Coupled PDE-ODEs Modeled Multi-Agent Systems
by Xu Ni, Kejia Yi, Yiming Jiang, Ancai Zhang and Chengdong Yang
Mathematics 2022, 10(2), 201; https://doi.org/10.3390/math10020201 - 10 Jan 2022
Cited by 5 | Viewed by 1709
Abstract
This paper discusses consensus control of nonlinear coupled parabolic PDE-ODE-based multi-agent systems (PDE-ODEMASs). First, a consensus controller of leaderless PDE-ODEMASs is designed. Based on a Lyapunov-based approach, coupling strengths are obtained for leaderless PDE-ODEMASs to achieve leaderless consensus. Furthermore, a consensus controller in [...] Read more.
This paper discusses consensus control of nonlinear coupled parabolic PDE-ODE-based multi-agent systems (PDE-ODEMASs). First, a consensus controller of leaderless PDE-ODEMASs is designed. Based on a Lyapunov-based approach, coupling strengths are obtained for leaderless PDE-ODEMASs to achieve leaderless consensus. Furthermore, a consensus controller in the leader-following PDE-ODEMAS is designed and the corresponding coupling strengths are obtained to ensure the leader-following consensus. Two examples show the effectiveness of the proposed methods. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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