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Nonlinear Control Systems with Recent Advances and Applications

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (31 May 2023) | Viewed by 17087

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Special Issue Editors


E-Mail Website1 Website2 Website3 Website4
Guest Editor
1. College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
2. Automated Systems & Soft Computing Lab (ASSCL), Prince Sultan University, Riyadh 12435, Saudi Arabia
3. Faculty of Computers and Artificial Intelligence, Benha University, Benha 13518, Egypt
Interests: control theory and applications; robotics; process control; artificial intelligence; machine learning, computational intelligence, dynamic system modeling
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Control and Systems Engineering, University of Technology, Baghdad 10001, Iraq
Interests: control theory; nonlinear control; robotic
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Electrical Engineering, College of Engineering, University of Baghdad, Al-Jadriyah, Baghdad 10001, Iraq
Interests: control theory; nonlinear control; robotic
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Electrical and Information Engineering, Università degli Studi di Cassino e del Lazio Meridionale, 03043 Cassino, FR, Italy
Interests: control systems: theory and applications; smart grid control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nonlinear control, such as robust stabilization and adaptive tracking, naturally arises when dealing with nonlinear controlled systems that may be subject to a variety of uncertainties and/or time-varying disturbances. Over the last few decades, tremendous progress has been made in the development of design methodologies for the control of nonlinear systems and their applications using various mathematical tools. Because there are many important and interesting challenges, the field of non-linear control systems has a bright future. Nonlinear control applications in energy, health care, robotics, biology, and big data research will advance both theory and technology adoption.

Although the literature contains a significant number of interesting and valuable results, the synthesis of control strategies for a broader class of nonlinear systems, as well as broader applications, remains challenging and open, particularly for the diversely complicated control tasks arising from the growing integration with emerging technologies in communication and computation areas. The proposed Special Issue's main goal is to present a cutting-edge collection of articles presenting novel developments in nonlinear control approaches in both theoretical background and applications. This Special Issue covers a variety of contributions from different fields.

Prof. Dr. Ahmad Taher Azar
Prof. Dr. Amjad J. Humaidi
Prof. Dr. Ibraheem Kasim Ibraheem
Prof. Dr. Giuseppe Fusco
Prof. Dr. Quanmin Zhu
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. Entropy is an international peer-reviewed open access monthly 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

  • backstepping control systems
  • bifurcations and bifurcating systems
  • bio-inspired control systems
  • fault tolerance control
  • fuzzy logic control
  • human–robot interaction for mobile robots
  • multiple mobile robot systems
  • nonlinear control design
  • nonlinear analysis for AI and optimization algorithms
  • nonlinear control of network-connected systems
  • observer design
  • output regulation and disturbance rejection
  • renewable energy control systems
  • robot navigation, localization and mapping
  • robust control
  • sensor-fusion-based control
  • sliding mode control systems
  • state/output feedback
  • time-delayed nonlinear dynamical systems

Published Papers (10 papers)

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Research

18 pages, 3608 KiB  
Article
An Incremental Broad-Learning-System-Based Approach for Tremor Attenuation for Robot Tele-Operation
by Guanyu Lai, Weizhen Liu, Weijun Yang, Huihui Zhong, Yutao He and Yun Zhang
Entropy 2023, 25(7), 999; https://doi.org/10.3390/e25070999 - 29 Jun 2023
Viewed by 870
Abstract
The existence of the physiological tremor of the human hand significantly affects the application of tele-operation systems in performing high-precision tasks, such as tele-surgery, and currently, the process of effectively eliminating the physiological tremor has been an important yet challenging research topic in [...] Read more.
The existence of the physiological tremor of the human hand significantly affects the application of tele-operation systems in performing high-precision tasks, such as tele-surgery, and currently, the process of effectively eliminating the physiological tremor has been an important yet challenging research topic in the tele-operation robot field. Some scholars propose using deep learning algorithms to solve this problem, but a large number of hyperparameters lead to a slow training speed. Later, the support-vector-machine-based methods have been applied to solve the problem, thereby effectively canceling tremors. However, these methods may lose the prediction accuracy, because learning energy cannot be accurately assigned. Therefore, in this paper, we propose a broad-learning-system-based tremor filter, which integrates a series of incremental learning algorithms to achieve fast remodeling and reach the desired performance. Note that the broad-learning-system-based filter has a fast learning rate while ensuring the accuracy due to its simple and novel network structure. Unlike other algorithms, it uses incremental learning algorithms to constantly update network parameters during training, and it stops learning when the error converges to zero. By focusing on the control performance of the slave robot, a sliding mode control approach has been used to improve the performance of closed-loop systems. In simulation experiments, the results demonstrated the feasibility of our proposed method. Full article
(This article belongs to the Special Issue Nonlinear Control Systems with Recent Advances and Applications)
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21 pages, 19987 KiB  
Article
A Cartesian-Based Trajectory Optimization with Jerk Constraints for a Robot
by Zhiwei Fan, Kai Jia, Lei Zhang, Fengshan Zou, Zhenjun Du, Mingmin Liu, Yuting Cao and Qiang Zhang
Entropy 2023, 25(4), 610; https://doi.org/10.3390/e25040610 - 03 Apr 2023
Cited by 1 | Viewed by 1443
Abstract
To address the time-optimal trajectory planning (TOTP) problem with joint jerk constraints in a Cartesian coordinate system, we propose a time-optimal path-parameterization (TOPP) algorithm based on nonlinear optimization. The key insight of our approach is the presentation of a comprehensive and effective iterative [...] Read more.
To address the time-optimal trajectory planning (TOTP) problem with joint jerk constraints in a Cartesian coordinate system, we propose a time-optimal path-parameterization (TOPP) algorithm based on nonlinear optimization. The key insight of our approach is the presentation of a comprehensive and effective iterative optimization framework for solving the optimal control problem (OCP) formulation of the TOTP problem in the (s,s˙)-phase plane. In particular, we identify two major difficulties: establishing TOPP in Cartesian space satisfying third-order constraints in joint space, and finding an efficient computational solution to TOPP, which includes nonlinear constraints. Experimental results demonstrate that the proposed method is an effective solution for time-optimal trajectory planning with joint jerk limits, and can be applied to a wide range of robotic systems. Full article
(This article belongs to the Special Issue Nonlinear Control Systems with Recent Advances and Applications)
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30 pages, 4729 KiB  
Article
A New Nonlinear Dynamic Speed Controller for a Differential Drive Mobile Robot
by Ibrahim A. Hameed, Luay Hashem Abbud, Jaafar Ahmed Abdulsaheb, Ahmad Taher Azar, Mohanad Mezher, Anwar Ja’afar Mohamad Jawad, Wameedh Riyadh Abdul-Adheem, Ibraheem Kasim Ibraheem and Nashwa Ahmad Kamal
Entropy 2023, 25(3), 514; https://doi.org/10.3390/e25030514 - 16 Mar 2023
Cited by 4 | Viewed by 1490
Abstract
A disturbance/uncertainty estimation and disturbance rejection technique are proposed in this work and verified on a ground two-wheel differential drive mobile robot (DDMR) in the presence of a mismatched disturbance. The offered scheme is the an improved active disturbance rejection control (IADRC) approach-based [...] Read more.
A disturbance/uncertainty estimation and disturbance rejection technique are proposed in this work and verified on a ground two-wheel differential drive mobile robot (DDMR) in the presence of a mismatched disturbance. The offered scheme is the an improved active disturbance rejection control (IADRC) approach-based enhanced dynamic speed controller. To efficiently eliminate the effect produced by the system uncertainties and external torque disturbance on both wheels, the IADRC is adopted, whereby all the torque disturbances and DDMR parameter uncertainties are conglomerated altogether and considered a generalized disturbance. This generalized disturbance is observed and cancelled by a novel nonlinear sliding mode extended state observer (NSMESO) in real-time. Through numerical simulations, various performance indices are measured, with a reduction of 86% and 97% in the ITAE index for the right and left wheels, respectively. Finally, these indices validate the efficacy of the proposed dynamic speed controller by almost damping the chattering phenomena and supplying a high insusceptibility in the closed-loop system against torque disturbance. Full article
(This article belongs to the Special Issue Nonlinear Control Systems with Recent Advances and Applications)
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16 pages, 3179 KiB  
Article
From Nonlinear Dominant System to Linear Dominant System: Virtual Equivalent System Approach for Multiple Variable Self-Tuning Control System Analysis
by Jinghui Pan, Kaixiang Peng and Weicun Zhang
Entropy 2023, 25(1), 173; https://doi.org/10.3390/e25010173 - 15 Jan 2023
Viewed by 1105
Abstract
The stability and convergence analysis of a multivariable stochastic self-tuning system (STC) is very difficult because of its highly nonlinear structure. In this paper, based on the virtual equivalent system method, the structural nonlinear or nonlinear dominated multivariable self-tuning system is transformed into [...] Read more.
The stability and convergence analysis of a multivariable stochastic self-tuning system (STC) is very difficult because of its highly nonlinear structure. In this paper, based on the virtual equivalent system method, the structural nonlinear or nonlinear dominated multivariable self-tuning system is transformed into a structural linear or linear dominated system, thus simplifying the stability and convergence analysis of multivariable STC systems. For the control process of a multivariable stochastic STC system, parameter estimation is required, and there may be three cases of parameter estimation convergence, convergence to the actual value and divergence. For these three cases, this paper provides four theorems and two corollaries. Given the theorems and corollaries, it can be directly concluded that the convergence of parameter estimation is a sufficient condition for the stability and convergence of stochastic STC systems but not a necessary condition, and the four theorems and two corollaries proposed in this paper are independent of specific controller design strategies and specific parameter estimation algorithms. The virtual equivalent system theory proposed in this paper does not need specific control strategies, parameters and estimation algorithms but only needs the nature of the system itself, which can judge the stability and convergence of the self-tuning system and relax the dependence of the system stability convergence criterion on the system structure information. The virtual equivalent system method proposed in this paper is proved to be effective when the parameter estimation may have convergence, convergence to the actual value and divergence. Full article
(This article belongs to the Special Issue Nonlinear Control Systems with Recent Advances and Applications)
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19 pages, 3545 KiB  
Article
Event-Triggered Tracking Control for Adaptive Anti-Disturbance Problem in Systems with Multiple Constraints and Unknown Disturbances
by Hong Shen, Qin Wang and Yang Yi
Entropy 2023, 25(1), 43; https://doi.org/10.3390/e25010043 - 27 Dec 2022
Viewed by 1167
Abstract
Aimed at the objective of anti-disturbance and reducing data transmission, this article discusses a novel dynamic neural network (DNN) modeling-based anti-disturbance control for a system under the framework of an event trigger. In order to describe dynamical characteristics of irregular disturbances, exogenous DNN [...] Read more.
Aimed at the objective of anti-disturbance and reducing data transmission, this article discusses a novel dynamic neural network (DNN) modeling-based anti-disturbance control for a system under the framework of an event trigger. In order to describe dynamical characteristics of irregular disturbances, exogenous DNN disturbance models with different excitation functions are firstly introduced. A novel disturbance observer-based adaptive regulation (DOBAR) method is then proposed, which can capture the dynamics of unknown disturbance. By integrating the augmented triggering condition and the convex optimization method, an effective anti-disturbance controller is then found to guarantee the system stability and the convergence of the output. Meanwhile, both the augmented state and the system output are constrained within given regions. Moreover, the Zeno phenomenon existing in event-triggered mechanisms is also successfully avoided. Simulation results for the A4D aircraft models are shown to verify the availability of the algorithm. Full article
(This article belongs to the Special Issue Nonlinear Control Systems with Recent Advances and Applications)
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22 pages, 9025 KiB  
Article
Design of Adaptive Fractional-Order Fixed-Time Sliding Mode Control for Robotic Manipulators
by Saim Ahmed, Ahmad Taher Azar and Mohamed Tounsi
Entropy 2022, 24(12), 1838; https://doi.org/10.3390/e24121838 - 16 Dec 2022
Cited by 14 | Viewed by 1667
Abstract
In this investigation, the adaptive fractional-order non-singular fixed-time terminal sliding mode (AFoFxNTSM) control for the uncertain dynamics of robotic manipulators with external disturbances is introduced. The idea of fractional-order non-singular fixed-time terminal sliding mode (FoFxNTSM) control is presented as the initial step. This [...] Read more.
In this investigation, the adaptive fractional-order non-singular fixed-time terminal sliding mode (AFoFxNTSM) control for the uncertain dynamics of robotic manipulators with external disturbances is introduced. The idea of fractional-order non-singular fixed-time terminal sliding mode (FoFxNTSM) control is presented as the initial step. This approach, which combines the benefits of a fractional-order parameter with the advantages of NTSM, gives rapid fixed-time convergence, non-singularity, and chatter-free control inputs. After that, an adaptive control strategy is merged with the FoFxNTSM, and the resulting model is given the label AFoFxNTSM. This is done in order to account for the unknown dynamics of the system, which are caused by uncertainties and bounded external disturbances. The Lyapunov analysis reveals how stable the closed-loop system is over a fixed time. The pertinent simulation results are offered here for the purposes of evaluating and illustrating the performance of the suggested scheme applied on a PUMA 560 robot. Full article
(This article belongs to the Special Issue Nonlinear Control Systems with Recent Advances and Applications)
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14 pages, 2163 KiB  
Article
Adaptive Fixed-Time Neural Networks Control for Pure-Feedback Non-Affine Nonlinear Systems with State Constraints
by Yang Li, Quanmin Zhu, Jianhua Zhang and Zhaopeng Deng
Entropy 2022, 24(5), 737; https://doi.org/10.3390/e24050737 - 22 May 2022
Cited by 1 | Viewed by 1611
Abstract
A new fixed-time adaptive neural network control strategy is designed for pure-feedback non-affine nonlinear systems with state constraints according to the feedback signal of the error system. Based on the adaptive backstepping technology, the Lyapunov function is designed for each subsystem. The neural [...] Read more.
A new fixed-time adaptive neural network control strategy is designed for pure-feedback non-affine nonlinear systems with state constraints according to the feedback signal of the error system. Based on the adaptive backstepping technology, the Lyapunov function is designed for each subsystem. The neural network is used to identify the unknown parameters of the system in a fixed-time, and the designed control strategy makes the output signal of the system track the expected signal in a fixed-time. Through the stability analysis, it is proved that the tracking error converges in a fixed-time, and the design of the upper bound of the setting time of the error system only needs to modify the parameters and adaptive law of the controlled system controller, which does not depend on the initial conditions. Full article
(This article belongs to the Special Issue Nonlinear Control Systems with Recent Advances and Applications)
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31 pages, 6269 KiB  
Article
Robust Variable-Step Perturb-and-Observe Sliding Mode Controller for Grid-Connected Wind-Energy-Conversion Systems
by Ilham Toumi, Billel Meghni, Oussama Hachana, Ahmad Taher Azar, Amira Boulmaiz, Amjad J. Humaidi, Ibraheem Kasim Ibraheem, Nashwa Ahmad Kamal, Quanmin Zhu, Giuseppe Fusco and Naglaa K. Bahgaat
Entropy 2022, 24(5), 731; https://doi.org/10.3390/e24050731 - 20 May 2022
Cited by 10 | Viewed by 2261
Abstract
In order to extract efficient power generation, a wind turbine (WT) system requires an accurate maximum power point tracking (MPPT) technique. Therefore, a novel robust variable-step perturb-and-observe (RVS-P&O) algorithm was developed for the machine-side converter (MSC). The control strategy was applied on a [...] Read more.
In order to extract efficient power generation, a wind turbine (WT) system requires an accurate maximum power point tracking (MPPT) technique. Therefore, a novel robust variable-step perturb-and-observe (RVS-P&O) algorithm was developed for the machine-side converter (MSC). The control strategy was applied on a WT based permanent-magnet synchronous generator (PMSG) to overcome the downsides of the currently published P&O MPPT methods. Particularly, two main points were involved. Firstly, a systematic step-size selection on the basis of power and speed measurement normalization was proposed; secondly, to obtain acceptable robustness for high and long wind-speed variations, a new correction to calculate the power variation was carried out. The grid-side converter (GSC) was controlled using a second-order sliding mode controller (SOSMC) with an adaptive-gain super-twisting algorithm (STA) to realize the high-quality seamless setting of power injected into the grid, a satisfactory power factor correction, a high harmonic performance of the AC source, and removal of the chatter effect compared to the traditional first-order sliding mode controller (FOSMC). Simulation results showed the superiority of the suggested RVS-P&O over the competing based P&O techniques. The RVS-P&O offered the WT an efficiency of 99.35%, which was an increase of 3.82% over the variable-step P&O algorithm. Indeed, the settling time was remarkably enhanced; it was 0.00794 s, which was better than for LS-P&O (0.0841 s), SS-P&O (0.1617 s), and VS-P&O (0.2224 s). Therefore, in terms of energy efficiency, as well as transient and steady-state response performances under various operating conditions, the RVS-P&O algorithm could be an accurate candidate for MPP online operation tracking. Full article
(This article belongs to the Special Issue Nonlinear Control Systems with Recent Advances and Applications)
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17 pages, 2462 KiB  
Article
Adaptive Orbital Rendezvous Control of Multiple Satellites Based on Pulsar Positioning Strategy
by Qiang Chen, Yong Zhao and Lixia Yan
Entropy 2022, 24(5), 575; https://doi.org/10.3390/e24050575 - 19 Apr 2022
Cited by 1 | Viewed by 1442
Abstract
This paper addresses the orbital rendezvous control for multiple uncertain satellites. Against the background of a pulsar-based positioning approach, a geometric trick is applied to determine the position of satellites. A discontinuous estimation algorithm using neighboring communications is proposed to estimate the target’s [...] Read more.
This paper addresses the orbital rendezvous control for multiple uncertain satellites. Against the background of a pulsar-based positioning approach, a geometric trick is applied to determine the position of satellites. A discontinuous estimation algorithm using neighboring communications is proposed to estimate the target’s position and velocity in the Earth’s Centered Inertial Frame for achieving distributed rendezvous control. The variables generated by the dynamic estimation are viewed as virtual reference trajectories for each satellite in the group, followed by a novel saturation-like adaptive control law with the assumption that the masses of satellites are unknown and time-varying. The rendezvous errors are proven to be convergent to zero asymptotically. Numerical simulations considering the measurement fluctuations validate the effectiveness of the proposed control law. Full article
(This article belongs to the Special Issue Nonlinear Control Systems with Recent Advances and Applications)
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12 pages, 1135 KiB  
Article
H Observer Based on Descriptor Systems Applied to Estimate the State of Charge
by Shengya Meng, Shihong Li, Heng Chi, Fanwei Meng and Aiping Pang
Entropy 2022, 24(3), 420; https://doi.org/10.3390/e24030420 - 17 Mar 2022
Cited by 6 | Viewed by 1841
Abstract
This paper proposes an H observer based on descriptor systems to estimate the state of charge (SOC). The battery’s open-current voltage is chosen as a generalized state variable, thereby avoiding the artificial derivative calculation of the algebraic equation for the SOC. Furthermore, [...] Read more.
This paper proposes an H observer based on descriptor systems to estimate the state of charge (SOC). The battery’s open-current voltage is chosen as a generalized state variable, thereby avoiding the artificial derivative calculation of the algebraic equation for the SOC. Furthermore, the observer’s dynamic performance is saved. To decrease the impacts of the uncertain noise and parameter perturbations, nonlinear H theory is implemented to design the observer. The sufficient conditions for the H observer to guarantee the disturbance suppression performance index are given and proved by the Lyapunov stability theory. This paper systematically gives the design steps of battery SOC H observers. The simulation results highlight the accuracy, transient performance, and robustness of the presented method. Full article
(This article belongs to the Special Issue Nonlinear Control Systems with Recent Advances and Applications)
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