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Distributed Coordination Control of Position-constrained Euler-Lagrangian Systems with Unknown Control Directions Under a Directed Graph

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  • Control Theory and Applications
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Abstract

For an actual control system, the position information is usually an indispensable physical quantity for feedback control, while in an actual project, the position quantity is generally constrained. This paper discusses the distributed leader-following consensus control problem of networked Euler-Lagrangian systems (ELSs) both with unknown control directions and position constrains under a directed topology. Two novel types of barrier Lyapunov functions together with a Nussbaum-type gain function are employed to design distributed leader-following consensus protocol under a directed graph in this paper. One Lyapunov function is used to ensure that all the signals in the closed-loop system are bounded and the other is designed to prove that the consensus tracking errors of all the followers are uniformly ultimately bounded (UUB) and can be adjusted arbitrarily small. Meanwhile, according to the analysis of the tracking procedure, the security problem of position constraints are always satisfied. Finally, simulation examples are given to verify the effectiveness of the proposed algorithms in this paper.

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Authors and Affiliations

  1. Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Luyan Xu & Chaoli Wang

  2. School of Electrical Engineering, Shanghai Dianji University, Shanghai, 201306, China

    Xuan Cai

  3. College of Marine Electrical Engineering, Dalian Maritime University, Dalian, China

    Shuanghe Yu & Yan Yan

  4. Institute of Machine Intelligence, University of Shanghai for Science and Technology, Shanghai, China

    Gang Wang

Authors
  1. Luyan Xu
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  2. Chaoli Wang
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  3. Xuan Cai
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  4. Shuanghe Yu
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  5. Yan Yan
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  6. Gang Wang
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Correspondence to Chaoli Wang.

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Declaration of Competing Interest

The authors declare that there is no competing financial interest or personal relationship that could have appeared to influence the work reported in this paper.

Luyan Xu received her B.Sc. degree in Henan Normal University in 2016. She is currently pursuing a Ph.D. degree in control science and engineering at the University of Shanghai for Science and Technology, Shanghai, China. Her research interests include distributed control of nonlinear systems, adaptive control, optimal control, and multi-agent systems.

Chaoli Wang received his B.Sc. and M.Sc. degrees from Mathematics Department, Lanzhou University, Lanzhou, China, in 1986 and 1992, respectively, and a Ph.D. degree in control theory and engineering from Beihang University, Beijing, China, in 1999. From 1999 to 2000, he was a Post-Doctoral Research Fellow with the Robotics Laboratory of Chinese Academy of Sciences, Shenyang, China. From 2001 to 2002, he was a Research Associate with the Department of Automation and Computer-Aided Engineering, the Chinese University of Hong Kong, Hong Kong. Since 2003, he has been a Professor with the School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai, China. His current research interests include nonlinear control, robust control, robot dynamic and control, visual serving feedback control, and pattern identification.

Xuan Cai received his B.Eng. degree in automation in 2012 from Shanghai Dianji University, Shanghai, China, and an M.Eng. degree in control engineering in 2015 and a Ph.D. degree in control science and engineering in 2020, both from the University of Shanghai for Science and Technology, Shanghai, China. He is currently a Lecturer with the School of Electrical Engineering, Shanghai Dianji University, Shanghai, China. His research interests include distributed control of nonlinear systems, adaptive control, and adaptive dynamic programming.

Shuanghe Yu received his bachelor’s degree in automatic control form Beijing Jiaotong University, and master’s degree in control theory and applications, and a Ph.D. degree in navigation, guidance and control both from Harbin Institute of Technology, China, in 1990, 1996, and 2001, respectively. From 2001 to 2003, he was a postdoctoral research fellow at Central Queensland University, Australia. From 2003 to 2004, he was a research fellow at Monash University, Australia. Since the autumn of 2004, he has been a Professor in the Department of Automation, Dalian Maritime University, China. His main research interests include nonlinear control theory and applications in multi-agent systems, marine vehicles, and other industrial process.

Yan Yan received her bachelor’s degree in automation, her master’s and Ph.D. degrees in control science and engineering from Dalian Maritime University, Dalian, China, in 2007, 2009, and 2013, respectively. From 2010 to 2012, she was a visiting Ph.D. student at RMIT University (Royal Melbourne Institute of Technology), Melbourne, Australia. From 2013 to 2015, she was a Post-Doctoral Fellow at Southeast University, Nanjing, China. She is currently an Associate Professor in the Department of Automation, Dalian Maritime University, Dalian, China. Her main research interests include nonlinear control theory and intelligent control.

Gang Wang received his B.Sc. degree in information and computing science and a Ph.D. degree in systems analysis and integration from the University of Shanghai for Science and Technology, Shanghai, China, in 2012 and 2017, respectively. From 2017 to 2019, he was a Research Associate with the Department of Electrical and Biomedical Engineering, University of Nevada, Reno, NV, USA. From 2021 to 2022, he was a Postdoctoral Fellow with the Hong Kong Centre for Logistics Robotics and the T Stone Robotics Institute, The Chinese University of Hong Kong, Hong Kong. He is currently an Associate Professor with the Institute of Machine Intelligence, University of Shanghai for Science and Technology, Shanghai, China. His research interests include distributed control of nonlinear systems, adaptive control, and robotics.

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This work was supported by the Natural Science Foundation of Shanghai under Grant (19ZR1436000) and National Defense Basic Research Program of China under Grant (JCKY2019413D001).

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Xu, L., Wang, C., Cai, X. et al. Distributed Coordination Control of Position-constrained Euler-Lagrangian Systems with Unknown Control Directions Under a Directed Graph. Int. J. Control Autom. Syst. 21, 2139–2153 (2023). https://doi.org/10.1007/s12555-021-0650-7

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