A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 3 Issue 3
Jul.  2016

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 7.847, Top 10% (SCI Q1)
    CiteScore: 13.0, Top 5% (Q1)
    Google Scholar h5-index: 64, TOP 7
Turn off MathJax
Article Contents
Mojtaba Naderi Soorki and Mohammad Saleh Tavazoei, "Constrained Swarm Stabilization of Fractional Order Linear Time Invariant Swarm Systems," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 3, pp. 320-331, 2016.
Citation: Mojtaba Naderi Soorki and Mohammad Saleh Tavazoei, "Constrained Swarm Stabilization of Fractional Order Linear Time Invariant Swarm Systems," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 3, pp. 320-331, 2016.

Constrained Swarm Stabilization of Fractional Order Linear Time Invariant Swarm Systems

Funds:

This work was supported by the Research Council of Sharif University of Technology under Grant (G930720).

  • This paper deals with asymptotic swarm stabilization of fractional order linear time invariant swarm systems in the presence of two constraints: the input saturation constraint and the restriction on distance of the agents from final destination which should be less than a desired value. A feedback control law is proposed for asymptotic swarm stabilization of fractional order swarm systems which guarantees satisfying the above-mentioned constraints. Numerical simulation results are given to confirm the efficiency of the proposed control method.

     

  • loading
  • [1]
    Zou A M, Kumar K D. Distributed attitude coordination control for spacecraft formation flying. IEEE Transactions on Aerospace and Electronic Systems, 2012, 48(2): 1329-1346
    [2]
    Olfati-Saber R, Murray R M. Distributed cooperative control of multiple vehicle formations using structural potential functions. In: Proceedings of the 15th IFAC World Congress. Barcelona, Spain: IFAC, 2002. 242
    [3]
    Su H S, Wang X F, Lin Z L. Flocking of multi-agents with a virtual leader. IEEE Transactions on Automatic Control, 2009, 54(2): 293-307
    [4]
    Cortés J, Bullo F. Coordination and geometric optimization via distributed dynamical systems. SIAM Journal on Control and Optimization, 2005, 44(5): 1543-1574
    [5]
    Olfati-Saber R, Murray R M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 2004, 49(9): 1520-1533
    [6]
    Tang Z J, Huang T Z, Shao J L, Hu J P. Consensus of second-order multiagent systems with nonuniform time-varying delays. Neurocomputing, 2012, 97: 410-414
    [7]
    Tian Y P, Zhang Y. High-order consensus of heterogeneous multi-agent systems with unknown communication delays. Automatica, 2012, 48(6): 1205-1212
    [8]
    Ren W. Consensus tracking under directed interaction topologies: algorithms and experiments. IEEE Transactions on Control Systems Technology, 2010, 18(1): 230-237
    [9]
    Xi J X, Shi Z Y, Zhong Y S. Consensus analysis and design for highorder linear swarm systems with time-varying delays. Physica A: Statistical Mechanics and its Applications, 2011, 390(23-24): 4114-4123
    [10]
    Magin R L. Fractional calculus models of complex dynamics in biological tissues. Computers and Mathematics with Applications, 2010, 59(5): 1586-1593
    [11]
    Cafagna D. Fractional calculus: a mathematical tool from the past for present engineers. IEEE Industrial Electronics Magazine, 2007, 1(2): 35-40
    [12]
    Cao Y, Li Y, Ren W, Chen Y Q. Distributed coordination of networked fractional-order systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B, Cybernetics, 2010, 40(2): 362-370
    [13]
    Song C, Cao J. Consensus of fractional-order linear systems. In: Proceedings of the 2013 9th Asian Control Conference. Istanbul, Turkey: IEEE, 2013. 1-4
    [14]
    Lu J Q, Shen J, Cao J D, Kurths J. Consensus of networked multiagent systems with delays and fractional-order dynamics. Consensus and Synchronization in Complex Networks. Berlin Heidelberg: Springer, 2013. 69-110
    [15]
    Yin X X, Yue D, Hu S L. Consensus of fractional-order heterogeneous multi-agent systems. IET Control Theory and Applications, 2013, 7(2): 314-322
    [16]
    Naderi Soorki M, Tavazoei M S. Fractional-order linear time invariant swarm systems: asymptotic swarm stability and time response analysis. Central European Journal of Physics, 2013, 11(6): 845-854
    [17]
    Sun W, Li Y, Li C P, Chen Y Q. Convergence speed of a fractional order consensus algorithm over undirected scale-free networks. Asian Journal of Control, 2011, 13(6): 936-946
    [18]
    Naderi Soorki M, Tavazoei M S. Adaptive consensus tracking for fractional-order linear time invariant swarm systems. Journal of Computational and Nonlinear Dynamics, 2014, 9(3): 031012
    [19]
    Shen J, Cao J, Lu J. Consensus of fractional-order systems with nonuniform input and communication delays. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2012, 226(2): 271-283
    [20]
    Shen J, Cao J D. Necessary and sufficient conditions for consensus of delayed fractional-order systems. Asian Journal of Control, 2012, 14(6): 1690-1697
    [21]
    Zheng Y S, Wang L. Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements. Systems and Control Letters, 2012, 61(8): 871-878
    [22]
    Yu W, Chen G, Cao M, Kurths J. Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2010, 40(3): 881-891
    [23]
    Wen G H, Duan Z S, Yu W W, Chen G R. Consensus in multi-agent systems with communication constraints. International Journal of Robust and Nonlinear Control, 2012, 22(2): 170-182
    [24]
    Han D K, Chesi G. Robust consensus for uncertain multi-agent systems with discrete-time dynamics. International Journal of Robust and Nonlinear Control, 2014, 24(13): 1858-1872
    [25]
    Li T, Zhang J F. Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises. IEEE Transactions on Automatic Control, 2010, 55(9): 2043-2057
    [26]
    Li Y, Xiang J, Wei W. Consensus problems for linear time-invariant multi-agent systems with saturation constraints. IET Control Theory and Applications, 2011, 5(6): 823-829
    [27]
    Meng Z Y, Zhao Z, Lin Z. On global consensus of linear multiagent systems subject to input saturation. In: Proceedings of the 2012 American Control Conference (ACC). Montreal, Canada: IEEE, 2012. 4516-4521
    [28]
    Geng H, Chen Z Q, Liu Z X, Zhang Q. Consensus of a heterogeneous multi-agent system with input saturation. Neurocomputing, 2015, 166: 382-388
    [29]
    Fan M C, Zhang H T, Li Z L. Distributed semiglobal consensus with relative output feedback and input saturation under directed switching networks. IEEE Transactions on Circuits and Systems II: Express Briefs, 2015, 62(8): 796-800
    [30]
    Wang Z Y, Gu D B, Meng T, Zhao Y Z. Consensus target tracking in multi-robot systems. Intelligent Robotics and Applications. Berlin Heidelberg: Springer, 2010. 724-735
    [31]
    Khoo S, Xie L, Man Z. Robust finite-time consensus tracking algorithm for multirobot systems. IEEE/ASME Transactions on Mechatronics, 2009, 14(2): 219-228
    [32]
    David S A, Balthazar J M, Julio B H S, Oliveira C. The fractionalnonlinear robotic manipulator: modeling and dynamic simulations. AIP Conference Proceedings, 2012, 1493(1): 298-305
    [33]
    Jezierski E, Ostalczyk P. Fractional-order mathematical model of pneumatic muscle drive for robotic applications. Robot Motion and Control 2009. London: Springer, 2009. 113-122
    [34]
    Sjöberg M, Kari L. Nonlinear isolator dynamics at finite deformations: an effective hyperelastic, fractional derivative, generalized friction model. Nonlinear Dynamics, 2003, 33(3): 323-336
    [35]
    Mendes R V, V´azquez L. The dynamical nature of a backlash system with and without fluid friction. Nonlinear Dynamics, 2007, 47(4): 363-366
    [36]
    Lim Y H, Oh K K, Ahn H S. Stability and stabilization of fractionalorder linear systems subject to input saturation. IEEE Transactions on Automatic Control, 2013, 58(4): 1062-1067
    [37]
    Podlubny I. Fractional Differential Equations. San Diego, CA: Academic Press, 1999.
    [38]
    Cai N, Xi J X, Zhong Y S. Swarm stability of high-order linear timeinvariant swarm systems. IET Control Theory and Applications, 20011, 5(2): 402-408
    [39]
    Godsil C, Royle G F. Algebraic Graph Theory. New York: Springer, 2001.
    [40]
    Caponetto R, Dongola G, Fortuna L, Petras I. Fractional Order Systems: Modeling and Control Applications. Hackensack, NJ: World Scientific, 2010.
    [41]
    Laub A J. Matrix Analysis for Scientists & Engineers. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics (SIAM), 2004.
    [42]
    Meyer C D. Matrix Analysis and Applied Linear Algebra. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics (SIAM), 2000.
    [43]
    Diethelm K, Ford N J, Freed A D. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics, 2002, 29(1-4): 3-22

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

    Article Metrics

    Article views (1051) PDF downloads(3) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return