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Frontiers of Electrical and Electronic Engineering in China 2008年第4期3卷 465-469页

作者： Zhengrong XIANG Weiming XIANG School of Automation Nanjing University of Science and TechnologyNanjing 210094China

The backstepping method is applied to a certain class of switched nonlinear systems to design state feedback controllers and a switching law based on multi-Lyapunov *** state feedback controllers and the switching law that can stabilize the system are *** switched nonlinear systems with uncertainties can be stabi-lized robustly by using the proposed ***,simu-lation results show the effectiveness of the method.

关键词： switched nonlinear systems backstepping method multi-Lyapunov functions robust stabilization

Function Projective Synchronization between Two Discrete-Time Hyperchaotic Systems Using backstepping method

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Applied Mathematics 2022年第2期13卷 178-190页

作者： Xin Li School of Mathematics and Statistics Changshu Institute of Technology Changshu China

We realize the function projective synchronization (FPS) between two discrete-time hyperchaotic systems, that is, the drive state vectors and the response state vectors can evolve in a proportional scaling function matrix. In this paper, a systematic scheme is explored to investigate the function projective synchronization of two identical discrete-time hyperchaotic systems using the backstepping method. Additionally, FPS of two different hyperchaotic systems is also realized. Numeric simulations are given to verify the effectiveness of our scheme.

关键词： Function Projective Synchronization Discrete-Time Hyperchaotic System backstepping method

Controller design for a Schr?dinger Equation with an input delay via backstepping method

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Controller design for a Schr?dinger Equation with an input d...

Adaptive backstepping Terminal Sliding Mode Control method Based on Recurrent Neural Networks for Autonomous Underwater Vehicle

第36届中国控制会议

作者： Dongyi Liu Rumeng Han Genqi Xu School of Mathematics Tianjin University

This paper is concerned with the controller design for a one dimensional Schr?dinger equation with an input delay on the boundary. A state-feedback control law is presented via the backstepping method to stabilize the... 详细信息

关键词： Schr?dinger Equation backstepping method State-Feedback Control Stability

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Chinese Journal of Mechanical Engineering 2018年第6期31卷 228-243页

作者： Chao Yang Feng Yao Ming-Jun Zhang College of Mechanical and Electrical Engineering Harbin Engineering University Harbin 150001 China

The trajectory tracking control problem is addressed for autonomous underwater vehicle(AUV) in marine environ?ment, with presence of the influence of the uncertain factors including ocean current disturbance, dynamic modeling uncertainty, and thrust model errors. To improve the trajectory tracking accuracy of AUV, an adaptive backstepping terminal sliding mode control based on recurrent neural networks(RNN) is proposed. Firstly, considering the inaccu?rate of thrust model of thruster, a Taylor’s polynomial is used to obtain the thrust model errors. And then, the dynamic modeling uncertainty and thrust model errors are combined into the system model uncertainty(SMU) of AUV; through the RNN, the SMU and ocean current disturbance are classified, approximated online. Finally, the weights of RNN and other control parameters are adjusted online based on the backstepping terminal sliding mode controller. In addition, a chattering?reduction method is proposed based on sigmoid function. In chattering?reduction method, the sigmoid function is used to realize the continuity of the sliding mode switching function, and the sliding mode switching gain is adjusted online based on the exponential form of the sliding mode function. Based on the Lyapu?nov theory and Barbalat’s lemma, it is theoretically proved that the AUV trajectory tracking error can quickly converge to zero in the finite time. This research proposes a trajectory tracking control method of AUV, which can e ectively achieve high?precision trajectory tracking control of AUV under the influence of the uncertain factors. The feasibility and e ectiveness of the proposed method is demonstrated with trajectory tracking simulations and pool?experi?ments of AUV.

关键词： Autonomous underwater vehicle(AUV) Trajectory tracking Neural networks backstepping method Terminal sliding mode Adaptive control

Event-Triggered-backstepping-Based Parallel Approaching Guidance method for Maneuvering Target Interception

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Guidance, Navigation and Control 2022年第1期2卷 77-100页

作者： Yaohua Shen Mou Chen Zixuan Zheng Hongzhen Guo College of Automation Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016P.R.China School of Astronautics National Key Laboratory of Aerospace Flight DynamicsNorthwestern Polytechnical UniversityXian 710072P.R.China

In order to achieve a straight ballistic trajectory of missile and reduce the update frequency of the missile normal acceleration for the interception of maneuvering target,a backstepping-based parallel approaching guidance method is designed with nonlinear disturbance observer(NDO)technique and event-triggered(ET)mechanism in this *** order to suppress the adverse e®ect of target maneuver,the NDO is designed to estimate the target maneuvering ***,the NDO-based backstepping method is used to obtain the normal acceleration of missile and realize the parallel approaching *** order to reduce the update frequency of missile normal acceleration,the ET mechanism is employed in the parallel approaching guidance *** the missile trajectory is relatively straight,the normal acceleration of missile remains *** the contrary,if the missile trajectory is not straight,the normal acceleration of missile is updated to make the missile trajectory *** this way,the ET-based parallel approaching guidance can be ***,a determined method for the initial missile°ight-path angle is proposed to keep the normal acceleration of missile at zero in the initial stage of ***,Lyapunov stability analysis method is used to prove that all signals in the closed-loop guidance system are uniformly ultimately ***,simulation results show the e®ectiveness of the proposed guidance method.

关键词： Parallel approaching guidance maneuvering target nonlinear disturbance observer event-triggered mechanism backstepping method

A new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning

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Journal of Automation and Intelligence 2024年第1期3卷 34-39页

作者： Wendi Chen Qinglai Wei Institute of Systems Engineering Macao University of Science and TechnologyAvenida WeiLong Taipa999078Macao Special Administrative Region of China The State Key Laboratory of Multimodal Artificial Intelligence Systems Institute of AutomationChinese Academy of Sciences95 Zhongguancun East Road100190BeijingChina

In this paper,a new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning is presented in this *** existence of nonlinear terms in the studied system makes it very difficult to design the optimal controller using traditional *** achieve optimal control,RL algorithm based on critic–actor architecture is considered for the nonlinear *** to the significant security risks of network transmission,the system is vulnerable to deception attacks,which can make all the system state *** using the attacked states to design coordinate transformation,the harm brought by unknown deception attacks has been *** presented control strategy can ensure that all signals in the closed-loop system are semi-globally ultimately ***,the simulation experiment is shown to prove the effectiveness of the strategy.

关键词： Nonlinear systems Reinforcement learning Optimal control backstepping method

backstepping Approach to the Adaptive Regulator Design for a One-Dimensional Wave Equation with General Input Harmonic Disturbance

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Journal of Systems Science & Complexity 2017年第2期30卷 253-279页

作者： GUO Wei SHAO Zhi-Chao Department of Applied Mathematics School of StatisticsUniversity of International Business and EconomicsBeijing 100029China

This paper considers the parameter estimation and stabilization of an unstable one-dimen- sional wave equation with matched general harmonic disturbance at the controlled end. The back- stepping method for infinite-dimensional system is adopted in the design of the adaptive regulator. It is shown that the resulting closed-loop system is asymptotically stable. Meanwhile, the estimated parameter is shown to be convergent to the unknown parameter as time unes tn ~n^nitv

关键词： backstepping method distributed parameter system disturbance rejection stability.

backstepping-based lag synchronization of a complex permanent magnet synchronous motor system

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Chinese Physics B 2013年第4期22卷 558-562页

作者：王兴元张昊 Faculty of Electronic Information and Electrical Engineering Dalian University of Technology

Through introducing the concept of complex current and resetting cross-coupling term, this paper proposes a novel complex permanent magnet synchronous motor system and analyzes its properties. Based on a complex permanent magnet synchronous motor system, we design controllers and achieve lag synchronizations both in real part and imaginary part with backstepping method. In our study, we take complex current, time delay, and structure of complex system into consideration. Numerical simulation results demonstrate the validity of controllers.

关键词： complex permanent magnet synchronous motor system time delay lag synchronization backstepping method

Output feedback adaptive control of multivariable nonlinear systems using Nussbaum gain method

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Journal of Systems Engineering and Electronics 2006年第4期17卷 829-835页

作者： Zhou Ying Wu Yuqiang Research Inst. of Automation Southeast Univ. Nanjing 210096 P. R. China Inst. of Automation Qufu Normal Univ. Qufu 273165 P. R. China

A new output feedback adaptive control scheme for multi-input and multi-output nonlinear systems with parametric uncertainty is presented based on the Nussbaum gain method and the backstepping approach. The high frequency gain matrix of the linear part of the system is not necessarily positive definite, but can be transformed into a lower or upper triangular matrix whose signs of diagonal dements are unknown. The new required condition for the high fi＇equency gain matrix can be easily checked for certain plants so that the proposed method is widely applicable. The global stability of the closed loop systems is guaranteed through this control scheme, at the same time the tracking error converges to zero.

关键词： backstepping method nussbaum gain global stability MIMO nonlincar systems.