A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Advanced Search
Volume 7 Issue 1
Jan.  2020

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 15.3, Top 1 (SCI Q1)
    CiteScore: 23.5, Top 2% (Q1)
    Google Scholar h5-index: 77， TOP 5
Turn off MathJax
Article Contents
Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2020  >  7(1): 292-300
Zhitao Li, Lixin Gao, Wenhai Chen and Yu Xu, "Distributed Adaptive Cooperative Tracking of Uncertain Nonlinear Fractional-order Multi-agent Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 292-300, Jan. 2020. doi: 10.1109/JAS.2019.1911858
Citation: Zhitao Li, Lixin Gao, Wenhai Chen and Yu Xu, "Distributed Adaptive Cooperative Tracking of Uncertain Nonlinear Fractional-order Multi-agent Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 292-300, Jan. 2020. doi: 10.1109/JAS.2019.1911858
shu

Distributed Adaptive Cooperative Tracking of Uncertain Nonlinear Fractional-order Multi-agent Systems

doi: 10.1109/JAS.2019.1911858
  • 1.

    Chen are with the Institute of Intelligent Systems and Decision, Wenzhou University, Zhejiang 325035, China

  • 2.

    College of Physics and Electronic Information Engineering, Wenzhou University, Wenzhou 325035, China

Funds:

the National Natural Science Foundation of China 61303211

Zhejiang Provincial Natural Science Foundation of China LY17F030003

Zhejiang Provincial Natural Science Foundation of China LY15F030009

More Information
    Abstract
  • In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network, an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight. With the developed control laws, we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded. Finally, a simple simulation example is provided to illustrate the established result.

     

    • FullText(HTML)
  • loading
    • Recommended by Associate Editor Yanjun Liu.
    References(39)
  • [1]
    W. Ren and Y. C. Cao, Distributed Coordination of Multi-agent Networks, Springer-Verlag London Limited, 2011.
    [2]
    Y. G. Hong, J. P. Hu, and L. X. Gao, " Tracking control for multi-agent consensus with an active leader and variable topology, " Automatica, vol. 42, no. 7, pp. 1177-1182, Jul. 2006. https://www.sciencedirect.com/science/article/pii/S0005109806001063
    [3]
    W. W. Yu, W. Ren, W. X. Zheng, G. R. Chen, and J. H. Lv, "Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics, " Automatica, vol. 58, no. 7, pp. 2107-2115, Jul. 2013. https://www.sciencedirect.com/science/article/pii/S000510981300174X
    [4]
    Y. Huo, Y. Lv, X. Wu, and Z. Duan, "Fully distributed consensus for general linear multi-agent systems with unknown external disturbances, " IET Control Theory & Applications, vol. 13, no. 16, pp. 2595-2609, Oct. 2019.
    [5]
    E. Arezou, A. Alfi, and H. Modares. "H$\infty$ consensus control of discrete-time multi-agent systems under network imperfections and external disturbance, " IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 667-675, May. 2019.
    [6]
    Y. Yamin, J. Huang, "Cooperative robust output regulation problem for discrete-time linear time-delay multi-agent systems, " Int. J. Robust and Nonlinear Control, vol. 28, no. 3, pp. 1035-1048, Feb. 2018.
    [7]
    Y. Lu, F. Liao, J. Deng, and C. Pattinson, "Cooperative optimal preview tracking for linear descriptor multi-agent systems, " J. Franklin Institute, vol.356, no. 2, pp. 908-934, Jan. 2019. https://www.sciencedirect.com/science/article/abs/pii/S0016003218300760
    [8]
    Y. Cao, Y. Li, W. Ren, and Y. Chen, "Distributed coordination of networked fractional-order systems, " IEEE Trans. Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 40, no. 2, pp. 362-370, Apr. 2010. http://med.wanfangdata.com.cn/Paper/Detail/PeriodicalPaper_PM19589747
    [9]
    Y. Zhang, H. Liang, H. Ma, Q. Zhou, and Z. Yu, "Distributed adaptive consensus tracking control for nonlinear multi-agent systems with state constraints, " Applied Mathematics and Computation, vol. 326, no. 1, pp. 16-32, Jan. 2018. https://www.sciencedirect.com/science/article/abs/pii/S0096300317309050
    [10]
    Y. Chang, Y. Wang, E. F. Alsaadi, and G. Zong, "Adaptive fuzzy output-feedback tracking control for switched stochastic pure-feedback nonlinear systems, " Int. J. Adaptive Control and Signal Processing, vol. 33, no. 10, pp. 1567-1582, Sep. 2019.
    [11]
    H. Ma, H. Liang, Q. Zhou, and C. Ahn, "Adaptive Dynamic Surface Control Design for Uncertain Nonlinear Strict-Feedback Systems With Unknown Control Direction and Disturbances, " IEEE Trans. Systems, Man, and Cybernetics: Systems, vol. 49, no. 3, pp. 506-515, Jan. 2018. https://ieeexplore.ieee.org/document/8419281/citations
    [12]
    Y. M. Li and S. C. Tong, Command-filtered-based fuzzy adaptive control design for MIMO switched nonstrict-feedback nonlinear systems, IEEE Trans. Fuzzy Systems, vol. 47, no. 4, pp. 1007-1016, 2017.
    [13]
    H. W. Zhang and F. L. Lewis, "Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics, " Automatica, vol. 48, no. 7, pp. 1432-1439, Jul. 2012. https://www.sciencedirect.com/science/article/pii/S0005109812001811
    [14]
    T. Yucelen and W. M. Haddad, "Low-frequency learning and fast adaptation in model reference adaptive control, " IEEE Trans. Autom. Control, vol. 58, no. 4, pp. 1080-1085, Apr. 2013. https://ieeexplore.ieee.org/document/6302181
    [15]
    Z. H. Peng, D. Wang, H. W. Zhang, G. Sun, and H. Wang, "Distributed model reference adaptive control for cooperative tracking of uncertain dynamical multi-agent systems, " IET Control Theory Applications, vol. 7, no. 8, pp. 1079-1087, May 2013.
    [16]
    Z. H. Peng, D. Wang, H. W. Wang, and W. Wang, "Distributed cooperative tracking of uncertain nonlinear multi-agent systems with fast learning, " Neurocomputing, vol. 129, no. 10, pp. 494-503, Apr. 2014 https://www.sciencedirect.com/science/article/abs/pii/S0925231213009144
    [17]
    Z. H. Peng, D. Wang, H. Zhang, and G. Sun, "Distributed neural network control for adaptive synchronization of uncertain dynamical multiagent systems, " IEEE Trans. Neural Networks and Learning Systems, vol. 25, no. 8, pp. 1508-1519, Aug. 2014. https://www.ncbi.nlm.nih.gov/pubmed/25050948
    [18]
    F. Wang, Z. Liu, Y. Zhang, and B. Chen, "Distributed adaptive coordination control for uncertain nonlinear multi-agent systems with dead-zone input, " J. Franklin Institute, vol. 353, no. 10, pp. 2270-2289, Jul. 2016. https://www.sciencedirect.com/science/article/abs/pii/S0016003216301090
    [19]
    J. Trigeassou, N. Maamri, J. Sabatier, and A. Oustaloup, "A Lyapunov approach to the stability of fractional differential equations, " Signal Processing, vol. 91, no. 3, pp. 437-445, Mar. 2011. https://www.sciencedirect.com/science/article/pii/S0165168410001854
    [20]
    C. P. Li and F. R. Zhang, "A survey on the stability of fractional differential equations, " European Physical J. Special Topics, vol. 193, no. 1, pp. 27-47, Mar. 2011. doi: 10.1140/epjst/e2011-01379-1
    [21]
    J. Gallegos and M. Duarte-Mermoud, "On the Lyapunov theory for fractional order systems, " Applied Mathematics and Computation, vol. 287, pp. 161-170, Sep. 2016. https://www.sciencedirect.com/science/article/abs/pii/S0096300316302892
    [22]
    J. W. Shen, J. D. Cao and J. Q. Lu, "Consensus of fractional-order systems with non-uniform input and communication delays, " Proc IMechE, Part Ⅰ, J. Systems and Control Engineering, vol. 226, no. 2, pp. 271-283, Aug. 2012.
    [23]
    X. X. Yin and S. L. Hu, "Consensus of fractional-order uncertain multi-agent systems based on output feedback, " Asian J. Control, vol. 15, no. 5, pp. 1538-1542, Sep. 2013. doi: 10.1002/asjc.683
    [24]
    J. W. Wang and X. H. Xiong, "A general fractional-order dynamical network: Synchronization behavior and state tuning, " Chaos, vol. 22, no. 2, pp. 023102(1-9), Jun. 2012. https://www.ncbi.nlm.nih.gov/pubmed/22757509
    [25]
    Z. Y. Yu, H. J. Jiang, and C. Hu, "Leader-following consensus of fractional-order multi-agent systems under fixed topology, " Neurocomputing, vol. 149, pp. 613-620, Feb. 2015. https://www.sciencedirect.com/science/article/abs/pii/S0925231214010273
    [26]
    Z. Y. Yu, H. J. Jiang, C. Hu, and J. Yu, "Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control, " International J. Control, vol. 88, pp. 1746-1756, Apr. 2015. doi: 10.1080/00207179.2015.1015807?journalCode=tcon20
    [27]
    J. Chen, Z. H. Guan, T. Li, D. X. Zhang, M. F. Ge, and D. F. Zheng, "Multiconsensus of fractional-order uncertain multi-agent systems, " Neurocomputing, vol. 149, pp. 698-705, Nov. 2015. http://xueshu.baidu.com/usercenter/paper/show?paperid=f6a041b7b11786f979082bdd4d419b13&site=xueshu_se&hitarticle=1
    [28]
    J. Chen, Z. H. Guan, C. Yang, T. Li, D. X. He, and X. H. Zhang, "Distributed containment control of fractional-order uncertain multi-agent systems, " J. Franklin Institute, vol. 353, no. 7, pp. 1672-1688, May 2016. https://www.sciencedirect.com/science/article/abs/pii/S0016003216000569
    [29]
    Z. K. Li, X. D. Liu, W. Ren, and L. H. Xie, "Distributed tracking control for linear multiagent systems with a leader of bounded unknown input, " IEEE Trans. Autom. Control, vol. 58, no. 2, pp. 518-523, Feb. 2013. https://ieeexplore.ieee.org/document/6237497
    [30]
    H. J. Chu, Y. Z. Cai, and W. D. Zhang, "Consensus tracking for multi-agent systems with directed graph via distributed adaptive protocol, " Neurocomputing, vol. 166, pp. 8-13, Oct. 2015. https://www.sciencedirect.com/science/article/abs/pii/S0925231215005263
    [31]
    B. Liu, X. L. Wang, H. S. Su, Y. P. Gao, and L. Wang, "Adaptive second-order consensus of multi-agent systems with heterogeneous nonlinear dynamics and time-varying delays, " Neurocomputing, vol. 118, pp. 289-300, Oct. 2013. https://www.sciencedirect.com/science/article/abs/pii/S0925231213004116
    [32]
    W. Wang, J. S. Huang, C. Y. Wen, and H. J. Fan, "Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots, " Automatica, vol. 50, no. 4, pp. 1254-1263, Apr. 2014. https://www.sciencedirect.com/science/article/pii/S0005109814000661
    [33]
    X. L. Xu, S. Y. Chen, and L. X. Gao, "Observer-based consensus tracking for second-order leader-following nonlinear multi-agent systems with adaptive coupling parameter design, " Neurocomputing, vol. 256, pp. 297-305, May 2015. doi: 10.1016/j.neucom.2014.12.037
    [34]
    Z. K. Li, W. Ren, X. D. Liu, and L. H. Xie, "Distributed consensus of linear multi-agent systems with adaptive dynamic protocols, " Automatica, vol. 49, no. 7, pp. 1986-1995, Jul. 2013. https://www.sciencedirect.com/science/article/pii/S0005109813001842
    [35]
    I. Podlubny, Fractional Differential Equations, New York: Academic Press, 1999.
    [36]
    W. M. Wonham, Linear Multivariable Contol, Springer-Verlag, New York, 2005.
    [37]
    S. J. Chung and J. J. E. Slotine, "Cooperative robot control and concurrent synchronization of Lagrangian systems, " IEEE Trans. Robotics, vol. 25, no. 3, pp. 686-700, Jun. 2009. https://ieeexplore.ieee.org/document/5068839
    [38]
    T. Kaczorek, "Positive linear systems consisting of $n$ subsystems with different fractional orders, " IEEE Trans. Circuits and Ssystems, vol. 58, no. 6, pp. 1203-1210, Jun. 2011.
    [39]
    R. K. H. Galvao, S. Hadjiloucas, K. H. Kienitz, H. M. Paiva, and R. J.M. Afonso, "Fractional order modeling of large three-dimensional RC networks, " IEEE Trans. Circuits and Systems, vol. 60, no. 3, pp. 624-637, Mar. 2013. https://ieeexplore.ieee.org/document/6365281
    • Related Articles
    • Supplements(0)

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(8)

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (1077) PDF downloads(91) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return