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Control Problem of Nonlinear Systems with Applications
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Control Problem of Nonlinear Systems with Applications

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

Deadline for manuscript submissions: closed (30 September 2022) | Viewed by 23474

Special Issue Editors

Prof. Dr. Rongwei Guo

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
Interests: chaos control; chaos synchronization; switched systems; nonlinear systems
Special Issues, Collections and Topics in MDPI journals
Dr. Cuimei Jiang

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
Interests: chaos control; chaos synchronization; nonlinear systems
Special Issues, Collections and Topics in MDPI journals
Dr. Ruimin Xu

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
Interests: stochastic control; stochastic differential equation; nonlinear systems; game theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The control problem of nonlinear systems with applications is general in the actual process, and they have attracted many scholars’ attention owing to the wide applications in various fields such as physics, mathematics, finance, transportation and engineer. Therefore, the analysis and synthesis of control problem play important roles in many practical systems.

The aim of this special issue is to bring together the latest/innovative knowledge and analysis and synthesis of control problem of nonlinear system. All the submissions are expected to have original ideas and novel approaches. We invite authors to contribute original research articles related to all aspects of this special issue.

Prof. Dr. Rongwei Guo
Dr. Cuimei Jiang
Dr. Ruimin Xu
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

  • chaos control
  • chaos synchronization
  • nonlinear systems
  • switched systems
  • stochastic control
  • stochastic differential equation

Published Papers (15 papers)

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Research

21 pages, 1318 KiB  
Article
Tan-Type BLF-Based Attitude Tracking Control Design for Rigid Spacecraft with Arbitrary Disturbances
by Nguyen Xuan-Mung, Mehdi Golestani and Sung-Kyung Hong
Mathematics 2022, 10(23), 4548; https://0-doi-org.brum.beds.ac.uk/10.3390/math10234548 - 01 Dec 2022
Cited by 6 | Viewed by 1216
Abstract
This study deals with the problem of disturbances in observer-based attitude tracking control for spacecraft in the presence of inertia-matrix uncertainty and arbitrary disturbance. Following the backstepping control, a tan-type barrier Lyapunov function (BLF)-based attitude tracking control method with prescribed settling time and [...] Read more.
This study deals with the problem of disturbances in observer-based attitude tracking control for spacecraft in the presence of inertia-matrix uncertainty and arbitrary disturbance. Following the backstepping control, a tan-type barrier Lyapunov function (BLF)-based attitude tracking control method with prescribed settling time and performance is systematically developed. The proposed control framework possesses three advantages over the existing attitude controllers. Firstly, the singularity problem associated with the use of fractional power in fixed-time control is effectively resolved without employing any command filter or piece-wise continuous function. Secondly, inspired by the concept of the tan-type BLF approach, any desired performance for the attitude tracking error is satisfied. Lastly, the total disturbance, including the system’s uncertainty, external disturbances, and time-derivative of the virtual control, is precisely reconstructed during a predefined time, even if the initial estimation error tends to infinity. Moreover, this time is determined as a tunable gain in the observer. The numerical simulations confirm the superior performance of the proposed control strategy in comparison with the existing pertinent works. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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12 pages, 359 KiB  
Article
Robust Stabilization of Impulsive Boolean Control Networks with Function Perturbation
by Qilong Sun and Haitao Li
Mathematics 2022, 10(21), 4029; https://0-doi-org.brum.beds.ac.uk/10.3390/math10214029 - 30 Oct 2022
Cited by 1 | Viewed by 849
Abstract
This paper studies the robust stabilization of impulsive Boolean control networks (IBCNs) with function perturbation. A Boolean control network (BCN) with a state-dependent impulsive sequence is converted to an equivalent BCN by the semi-tensor product method. Based on the equivalence of stabilization between [...] Read more.
This paper studies the robust stabilization of impulsive Boolean control networks (IBCNs) with function perturbation. A Boolean control network (BCN) with a state-dependent impulsive sequence is converted to an equivalent BCN by the semi-tensor product method. Based on the equivalence of stabilization between the IBCN and the corresponding BCN, several criteria are proposed for the robust stabilization of IBCNs. Furthermore, when the IBCN is not robustly stabilizable after the function perturbation, an algorithm is presented to modify the control or the impulse-triggered set. Finally, an example is given to verify the obtained results. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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21 pages, 6554 KiB  
Article
Trajectory Tracking Design for a Swarm of Autonomous Mobile Robots: A Nonlinear Adaptive Optimal Approach
by Yung-Hsiang Chen and Yung-Yue Chen
Mathematics 2022, 10(20), 3901; https://0-doi-org.brum.beds.ac.uk/10.3390/math10203901 - 20 Oct 2022
Cited by 5 | Viewed by 1458
Abstract
This research presents a nonlinear adaptive optimal control approach to the trajectory tracking problem of a swarm of autonomous mobile robots. Mathematically, finding an analytical adaptive control solution that meets the H2 performance index for the trajectory tracking problem when controlling a [...] Read more.
This research presents a nonlinear adaptive optimal control approach to the trajectory tracking problem of a swarm of autonomous mobile robots. Mathematically, finding an analytical adaptive control solution that meets the H2 performance index for the trajectory tracking problem when controlling a swarm of autonomous mobile robots is an almost impossible task, due to the great complexity and high dimensions of the dynamics. For deriving an analytical adaptive control law for this tracking problem, a particular formulation for the trajectory tracking error dynamics between a swarm of autonomous mobile robots and the desired trajectory is made via a filter link. Based on this prior analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from a high-dimensional nonlinear partial differential equation, which is equivalent to solving the trajectory tracking problem of a swarm of autonomous mobile robots with respect to an H2 performance index. This delivered adaptive nonlinear control solution offers the advantages of a simple control structure and good energy-saving performance. From the trajectory tracking verification, this proposed control approach possesses satisfactory trajectory tracking performance for a swarm of autonomous mobile robots, even under the effects of huge modeling uncertainties. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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14 pages, 1169 KiB  
Article
Partial Anti-Synchronization Problem of the 4D Financial Hyper-Chaotic System with Periodically External Disturbance
by Lin Cao and Rongwei Guo
Mathematics 2022, 10(18), 3373; https://0-doi-org.brum.beds.ac.uk/10.3390/math10183373 - 16 Sep 2022
Cited by 10 | Viewed by 884
Abstract
This paper is concerned with the partial anti-synchronization of the 4D financial hyper-chaotic system with periodically external disturbance. Firstly, the existence of the partial anti-synchronization problem for the nominal 4D financial system is proven. Then, a suitable filter is presented, by which the [...] Read more.
This paper is concerned with the partial anti-synchronization of the 4D financial hyper-chaotic system with periodically external disturbance. Firstly, the existence of the partial anti-synchronization problem for the nominal 4D financial system is proven. Then, a suitable filter is presented, by which the periodically external disturbance is asymptotically estimated. Moreover, two disturbance estimator (DE)-based controllers are designed to realize the partial anti-synchronization problem of such a system. Finally, numerical simulation verifies the effectiveness and correctness of the proposed results. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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16 pages, 2282 KiB  
Article
A Novel Nonsingular Terminal Sliding Mode Observer-Based Sensorless Control for Electrical Drive System
by Yongjie Yang and Xudong Liu
Mathematics 2022, 10(17), 3123; https://0-doi-org.brum.beds.ac.uk/10.3390/math10173123 - 31 Aug 2022
Cited by 1 | Viewed by 1219
Abstract
To improve the sensorless control performance of electrical drive systems, a nonsingular terminal sliding mode observer (NTSMO) and adaptive observer are proposed to solve the chattering and phase delay problems. Firstly, by defining a new nonsingular terminal sliding mode surface, the sliding mode [...] Read more.
To improve the sensorless control performance of electrical drive systems, a nonsingular terminal sliding mode observer (NTSMO) and adaptive observer are proposed to solve the chattering and phase delay problems. Firstly, by defining a new nonsingular terminal sliding mode surface, the sliding mode observer based on the fast reaching law is designed to estimate the back electromotive force (EMF). The observer enhances the robustness and system performance eliminates the singularity and attenuates the chattering. Next, to obtain the accurate back-EMF signal, an adaptive observer is designed instead of a traditional low-pass filter to filter out the harmonics. The adaptive observer can avoid the phase delay problem and further improve the signal observation accuracy. Then, the rotor position and speed information are accurately tracked. The proposed method is applied to the speed control system of a permanent magnet synchronous motor (PMSM), and the effectiveness and feasibility of the proposed sliding mode observer are demonstrated by the experiment. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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15 pages, 4246 KiB  
Article
Gain-Scheduled Sliding-Mode-Type Iterative Learning Control Design for Mechanical Systems
by Qijia Yao, Hadi Jahanshahi, Stelios Bekiros, Sanda Florentina Mihalache and Naif D. Alotaibi
Mathematics 2022, 10(16), 3005; https://0-doi-org.brum.beds.ac.uk/10.3390/math10163005 - 20 Aug 2022
Cited by 8 | Viewed by 1389
Abstract
In this paper, a novel gain-scheduled sliding-mode-type (SM-type) iterative learning (IL) control approach is proposed for the high-precision trajectory tracking of mechanical systems subject to model uncertainties and disturbances. Based on the SM variable, the proposed controller is synthesized involving a feedback regulation [...] Read more.
In this paper, a novel gain-scheduled sliding-mode-type (SM-type) iterative learning (IL) control approach is proposed for the high-precision trajectory tracking of mechanical systems subject to model uncertainties and disturbances. Based on the SM variable, the proposed controller is synthesized involving a feedback regulation item, a feedforward learning item, and a robust switching item. The feedback regulation item is adopted to regulate the position and velocity tracking errors, the feedforward learning item is applied to handle the model uncertainties and repetitive disturbance, and the robust switching item is introduced to compensate the nonrepetitive disturbance and linearization residual error. Moreover, the gain-scheduled mechanism is employed for both the feedback regulation item and feedforward learning item to enhance the convergence speed. Convergence analysis illustrates that the position and velocity tracking errors can eventually regulate to zero under the proposed controller. By combining the advantages of both SM control and IL control, the proposed controller has strong robustness against model uncertainties and disturbances. Lastly, simulations and comparisons are provided to evaluate the efficiency and excellent performance of the proposed control approach. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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13 pages, 2059 KiB  
Article
Adaptive Neural Tracking Control for Nonstrict-Feedback Nonlinear Systems with Unknown Control Gains via Dynamic Surface Control Method
by Xiongfeng Deng, Yiming Yuan, Lisheng Wei, Binzi Xu and Liang Tao
Mathematics 2022, 10(14), 2419; https://0-doi-org.brum.beds.ac.uk/10.3390/math10142419 - 11 Jul 2022
Cited by 2 | Viewed by 1166
Abstract
This paper addresses the tracking control problem of nonstrict-feedback systems with unknown control gains. The dynamic surface control method, Nussbaum gain function control technique, and radial basis function neural network are applied for the design of virtual control laws, and adaptive control laws. [...] Read more.
This paper addresses the tracking control problem of nonstrict-feedback systems with unknown control gains. The dynamic surface control method, Nussbaum gain function control technique, and radial basis function neural network are applied for the design of virtual control laws, and adaptive control laws. Then, an adaptive neural tracking control law is proposed in the last step. By using the dynamic surface control method, the “explosion of complexity” problem of conventional backstepping is avoided. Based on the application of the Nussbaum gain function control technique, the unknown control gain problem is well solved. With the help of the radial basis function neural network, the unknown nonlinear dynamics are approximated. Furthermore, through Lyapunov stability analysis, it is proved that the proposed control law can guarantee that all signals in the closed-loop system are bounded and the tracking error can converge to an arbitrarily small domain of zero by adjusting the design parameters. Finally, two examples are provided to illustrate the effectiveness of the proposed control law. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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15 pages, 2119 KiB  
Article
Observer-Based Finite-Time H∞ Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model
by Zhiguo Yan, Zhiwei Zhang, Guolin Hu and Baolong Zhu
Mathematics 2022, 10(12), 2102; https://0-doi-org.brum.beds.ac.uk/10.3390/math10122102 - 17 Jun 2022
Cited by 1 | Viewed by 1308
Abstract
This paper studies the problem of the finite-time H∞ control of the blood gases system, presented as a T-S fuzzy model with bounded disturbance during extracorporeal circulation. The aim was to design an observer-based fuzzy controller to ensure that the closed-loop system [...] Read more.
This paper studies the problem of the finite-time H∞ control of the blood gases system, presented as a T-S fuzzy model with bounded disturbance during extracorporeal circulation. The aim was to design an observer-based fuzzy controller to ensure that the closed-loop system was finite-time bounded with the H∞ performance. Firstly, different from the existing results, the T-S fuzzy model of a blood gas control system was developed and a new method was given to process the time derivatives of the membership functions. Secondly, based on the fuzzy Lyapunov function, sufficient conditions for the H∞ finite-time boundedness of the system were obtained by using Finsler’s lemma and matrix decoupling techniques. Simulation results are provided to demonstrate the effectiveness of the proposed methodology. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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21 pages, 3629 KiB  
Article
Sliding Mode Control of Manipulator Based on Improved Reaching Law and Sliding Surface
by Peng Ji, Chenglong Li and Fengying Ma
Mathematics 2022, 10(11), 1935; https://0-doi-org.brum.beds.ac.uk/10.3390/math10111935 - 05 Jun 2022
Cited by 11 | Viewed by 2541
Abstract
Aiming at the problem of convergence speed and chattering in sliding mode variable structure control of manipulator, an improved exponential reaching law and nonlinear sliding surface are proposed, and the Lyapunov function is used to analyze its stability. According to the dynamic model [...] Read more.
Aiming at the problem of convergence speed and chattering in sliding mode variable structure control of manipulator, an improved exponential reaching law and nonlinear sliding surface are proposed, and the Lyapunov function is used to analyze its stability. According to the dynamic model of the 6-DOF UR5 manipulator and the proposed reaching law and sliding surface, the corresponding control scheme is designed. The control performance of the proposed control scheme is verified by tracking the end trajectory of the manipulator on the MATLAB and CoppeliaSim robot simulation platform. The experimental results show that the proposed control scheme can not only significantly improve the convergence speed and make the system converge quickly, but also can effectively reduce the chattering of the system. Even in the presence of disturbance signals, fast and stable tracking can be achieved while ensuring the robustness of the system, and the chattering of the robotic arm system can be weakened to a certain extent. Compared with the classical control method based on the computational torque method and the traditional sliding mode control scheme based on the exponential reaching law, the proposed scheme has certain advantages in terms of tracking accuracy, convergence speed, and reducing system chattering, and effectively improves the overall control performance of the system. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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19 pages, 1697 KiB  
Article
Human Alertness Optimization with a Three-Process Dynamic Model
by Jiawei Yin, Agung Julius, John T. Wen, Zhen Wang, Chuanlin He and Lei Kou
Mathematics 2022, 10(11), 1916; https://0-doi-org.brum.beds.ac.uk/10.3390/math10111916 - 02 Jun 2022
Cited by 1 | Viewed by 1550
Abstract
Circadian rhythm is an important biological process for humans as it modulates a wide range of physiological processes, including body temperature, sleep-wake cycle, and cognitive performance. As the most powerful external stimulus of circadian rhythm, light has been studied as a zeitgeber to [...] Read more.
Circadian rhythm is an important biological process for humans as it modulates a wide range of physiological processes, including body temperature, sleep-wake cycle, and cognitive performance. As the most powerful external stimulus of circadian rhythm, light has been studied as a zeitgeber to regulate the circadian phase and sleep. This paper addresses the human alertness optimization problem, by optimizing light exposure and sleep schedules to relieve fatigue and cognitive impairment, in cases of night-shift workers and subjects with certain mission periods based on dynamics of the circadian rhythm system. A three-process hybrid dynamic model is used for simulating the circadian rhythm and predicting subjective alertness and sleepiness. Based on interindividual difference in sleep type and living habits, we propose a tunable sleep schedule in the alertness optimization problem, which allows the appropriate tuning of sleep and wake times based on sleep propensity. Variational calculus is applied to evaluate the impacts of light and sleep schedules on the alertness and a gradient descent algorithm is proposed to determine the optimal solutions to maximize the alertness level in various cases. Numerical simulation results demonstrate that the cognitive performance during certain periods can be significantly improved by optimizing the light input and tuning sleep/wake times compared to empirical data. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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17 pages, 4842 KiB  
Article
Sliding Mode Controller Based on the Extended State Observer for Plant-Protection Quadrotor Unmanned Aerial Vehicles
by Fengying Ma, Zhe Yang and Peng Ji
Mathematics 2022, 10(8), 1346; https://0-doi-org.brum.beds.ac.uk/10.3390/math10081346 - 18 Apr 2022
Cited by 7 | Viewed by 1792
Abstract
Owing to the complex dynamics of quadrotor unmanned aerial vehicles (UAVs) and their susceptibility to unknown interferences in an actual working environment, the flight control accuracy of UAVs is extremely high. Moreover, their anti-interference ability is particularly important. This study designed a sliding-mode [...] Read more.
Owing to the complex dynamics of quadrotor unmanned aerial vehicles (UAVs) and their susceptibility to unknown interferences in an actual working environment, the flight control accuracy of UAVs is extremely high. Moreover, their anti-interference ability is particularly important. This study designed a sliding-mode controller based on the extended state observer. The position control was obtained through the outer-loop position controller. The attitude control was determined through the inner-loop attitude controller. The input of the UAV system was obtained through the controller. The boundary-layer function was used to weaken the oscillatory response of the system, and the traditional extended state observer was improved to improve the response speed, robustness, and tracking accuracy of the controller. For the entire process, the input and output state information of the system and total internal and external disturbances were estimated in real-time through the extended state observer. A sliding-mode control law was designed to compensate for the estimated disturbance in real-time to realize attitude control. Finally, Lyapunov theory was used to confirm the stability of the system. The simulation results demonstrated the improved anti-interference and tracking ability of the designed controller. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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25 pages, 7014 KiB  
Article
Static and Dynamic Analysis of 6-DOF Quasi-Zero-Stiffness Vibration Isolation Platform Based on Leaf Spring Structure
by Zhen Wang, Chuanlin He, Yan Xu, Dong Li, Zhanyuan Liang, Wei Ding and Lei Kou
Mathematics 2022, 10(8), 1342; https://0-doi-org.brum.beds.ac.uk/10.3390/math10081342 - 18 Apr 2022
Cited by 3 | Viewed by 2085
Abstract
Multi-degree-of-freedom isolator with low stiffness is a fair prospect in engineering application. In this paper, a novel 6-DOF QZS vibration isolation platform based on leaf spring structure is presented. Its bearing capacity is provided through four leaf springs, and the quasi-zero-stiffness is realized [...] Read more.
Multi-degree-of-freedom isolator with low stiffness is a fair prospect in engineering application. In this paper, a novel 6-DOF QZS vibration isolation platform based on leaf spring structure is presented. Its bearing capacity is provided through four leaf springs, and the quasi-zero-stiffness is realized by the force balance between the central spring and the suspension spring. 6-DOF vibration isolation is realized by the ball-hinge fixed design of a leaf spring. Through static and dynamic analysis, the following conclusions are brought. The stiffness of the leaf spring and the deformation of the central spring under static load are directly proportional to the bearing capacity of the isolation table. Besides, in order to ensure that the stiffness of the system is close to zero, the stiffness of the suspension spring and the inner spring should be as similar as possible. The vertical and horizontal displacement transmissibility tests of the isolation platform are carried out, in which the jumping phenomenon in the QZS vibration isolation platform is analyzed. By improving the damping of the structure and the length of the suspension spring, the dynamic vibration isolation process of the system can be more stable, the transmissibility can be reduced, and the vibration isolation effect can be enhanced. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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15 pages, 4476 KiB  
Article
Several Control Problems of a Class of Complex Nonlinear Systems Based on UDE
by Zuoxun Wang, Wenzhu Zhang, Lei Ma and Guijuan Wang
Mathematics 2022, 10(8), 1313; https://0-doi-org.brum.beds.ac.uk/10.3390/math10081313 - 14 Apr 2022
Viewed by 999
Abstract
This paper mainly studies several control problems of a complex 4D chaotic system. Firstly, the real part and imaginary part of the complex 4D chaotic system are separated, and the system is equivalent to a six-dimensional continuous autonomous real chaotic system. Then, the [...] Read more.
This paper mainly studies several control problems of a complex 4D chaotic system. Firstly, the real part and imaginary part of the complex 4D chaotic system are separated, and the system is equivalent to a six-dimensional continuous autonomous real chaotic system. Then, the stabilization, synchronization, and anti-synchronization of the complex four-dimensional chaotic system are realized by using the control method of the combination of dynamic feedback gain control and UDE control, and the corresponding physical controllers are designed respectively. Finally, the correctness and effectiveness of the theoretical results are verified by numerical simulation. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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23 pages, 2903 KiB  
Article
Active Disturbance Rejection Terminal Sliding Mode Control for Tele-Aiming Robot System Using Multiple-Model Kalman Observers
by Peng Ji, Feng Min, Fengying Ma, Fangfang Zhang and Dejing Ni
Mathematics 2022, 10(8), 1268; https://0-doi-org.brum.beds.ac.uk/10.3390/math10081268 - 11 Apr 2022
Cited by 1 | Viewed by 1349
Abstract
This study proposes a tele-aiming control strategy for the ground reconnaissance robot to track the maneuvering target rapidly in the presence of dynamic uncertainties, sensory measurement noises, and time-varying external disturbances. First, the tele-aiming control trajectory generated by human–computer interaction (HCI) device is [...] Read more.
This study proposes a tele-aiming control strategy for the ground reconnaissance robot to track the maneuvering target rapidly in the presence of dynamic uncertainties, sensory measurement noises, and time-varying external disturbances. First, the tele-aiming control trajectory generated by human–computer interaction (HCI) device is filtered with a tracking differentiator and a recursive average filter. Second, the inertial impact force disturbance generated by maneuvering tele-aiming control jointly with the other uncertainties (e.g., internal friction, modeling error, etc.) is considered as a lumped disturbance, and then a novel multiple-model augmented-state extended Kalman observer (MEKO) is designed, capable of filtering out the joint measurement noises and estimating the lumped disturbance simultaneously. Lastly, a nonsingular terminal sliding mode controller is applied to eliminate the lumped disturbance and control the joints to track the corresponding desired joint trajectory. To verify the tele-aiming control performance, the random trajectory tracking experiments are designed to simulate the tele-aiming tracking control of maneuvering targets. As indicated from the experimental results, the proposed control strategy is capable of significantly suppressing the effect of inertial impact force disturbance and joint measurement noises, and achieving fast and stable tele-aiming control. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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20 pages, 8420 KiB  
Article
A New Synchronization Method for Time-Delay Fractional Complex Chaotic System and Its Application
by Junmei Guo, Chunrui Ma, Xinheng Wang, Fangfang Zhang, Michaël Antonie van Wyk and Lei Kou
Mathematics 2021, 9(24), 3305; https://0-doi-org.brum.beds.ac.uk/10.3390/math9243305 - 18 Dec 2021
Cited by 2 | Viewed by 1964
Abstract
This paper proposes a class of time-delay fractional complex Lu¨ system and utilizes the adomian decomposition algorithm to study the dynamics of the system. Firstly, the time chaotic attractor, coexistence attractor and parameter space are studied. The bifurcation diagram and complexity [...] Read more.
This paper proposes a class of time-delay fractional complex Lu¨ system and utilizes the adomian decomposition algorithm to study the dynamics of the system. Firstly, the time chaotic attractor, coexistence attractor and parameter space are studied. The bifurcation diagram and complexity are used to analyze the dynamic characteristics of the system. Secondly, the definition of modified fractional projective difference function synchronization (MFPDFS) is introduced. The corresponding synchronous controller is designed to realize the MFPDFS of the time-delay fractional complex Lu¨ system. Thirdly, based on the background of wireless speech communication system (WSCs), the MFPDFS controller is used to realize the secure speech transmission. Finally, the effectiveness of the controller is verified by numerical simulation. The signal-noise ratio (SNR) analysis of speech transmission is given. The performance of secure communication is verified by numerical simulation. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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