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 1 Issue 1
Jan.  2014

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 6.171, Top 11% (SCI Q1)
    CiteScore: 11.2, Top 5% (Q1)
    Google Scholar h5-index: 51, TOP 8
Turn off MathJax
Article Contents
Tengfei Liu and Zhongping Jiang, "Distributed Control of Nonlinear Uncertain Systems: A Cyclic-small-gain Approach," IEEE/CAA J. of Autom. Sinica, vol. 1, no. 1, pp. 46-53, 2014.
Citation: Tengfei Liu and Zhongping Jiang, "Distributed Control of Nonlinear Uncertain Systems: A Cyclic-small-gain Approach," IEEE/CAA J. of Autom. Sinica, vol. 1, no. 1, pp. 46-53, 2014.

Distributed Control of Nonlinear Uncertain Systems: A Cyclic-small-gain Approach

Funds:

This work was supported by US National Science Foundation (DMS-0906659, EC CS-1230040).

  • This paper presents a cyclic-small-gain approach to distributed control of nonlinear multi-agent systems for output agreement. Through a novel nonlinear control law design, the output agreement problem is transformed into a stabilization problem, and the closed-loop multi-agent system is transformed into a large-scale system composed of input-to-state stability (ISS) subsystems which are interconnected with each other through redefined outputs. By forcing the redefined outputs to go to arbitrarily small neighborhoods of the origin, practical consensus is achieved for the agents in the sense that their outputs ultimately converge to each other within an arbitrarily small region. A recently developed cyclic-small-gain result is adopted to assign appropriately the ISS gains to the transformed interconnected system. Moreover, if the system is disturbancefree, then consensus can be guaranteed. Interestingly, the closedloop multi-agent system is also robust to bounded time-delays and disturbances in information exchange.

     

  • loading
  • [1]
    Ogren P, Egerstedt M, Hu X M. A control Lyapunov function approach to multiagent coordination. IEEE Transactions on Robotics and Automation, 2002, 18(5):847-851
    [2]
    Lin Z Y, Francis B, Maggiore M. State agreement for continuous-time coupled nonlinear systems. SIAM Journal on Control and Optimization, 2007, 46(1):288-307
    [3]
    Shi G D, Hong Y G. Global target aggregation and state agreement of nonlinear multi-agent systems with switching topologies. Automatica, 2009, 45(5):1165-1175
    [4]
    Liu S, Xie L H, Zhang H S. Distributed consensus for multi-agent systems with delays and noises in transmission channels. Automatica, 2011, 47(5):920-934
    [5]
    Arcak M. Passivity as a design tool for group coordination. IEEE Transactions on Automatic Control, 2007, 52(8):1380-1390
    [6]
    Fax J A, Murray R M. Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control, 2004, 49(9):1465-1476
    [7]
    Cortes J, Martinez S, Bullo F. Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Transactions on Automatic Control, 2006, 51(8):1289-1298
    [8]
    Siljak D D. Dynamic graphs. Nonlinear Analysis:Hybrid Systems, 2008, 2(2):544-567
    [9]
    Qu Z H, Wang J, Hull R A. Cooperative control of dynamical systems with application to autonomous vehicles. IEEE Transactions on Automatic Control, 2008, 53(4):894-911
    [10]
    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
    [11]
    Li T, Fu M Y, Xie L H, Zhang J F. Distributed consensus with limited communication data rate. IEEE Transactions on Automatic Control, 2011, 56(2):279-292
    [12]
    Wang X L, Hong Y G, Huang J, Jiang Z P. A distributed control approach to a robust output regulation problem for multi-agent systems. IEEE Transactions on Automatic Control, 2010, 55(12):2891-2895
    [13]
    Wieland P, Sepulchre R, Allgower F. An internal model principle is necessary and sufficient for linear output synchronization. Automatica, 2011, 47(5):1068-1074
    [14]
    Su Y, Huang J. Cooperative output regulation of linear multi-agent systems. IEEE Transactions on Automatic Control, 2012, 57(4):1062-1066
    [15]
    Ogren P, Fiorelli E, Leonard N E. Cooperative control of mobile sensor networks:adaptive gradient climbing in a distributed environment. IEEE Transactions on Automatic Control, 2004, 49(8):1292-1302
    [16]
    Tanner H G, Jadbabaie A, Pappas G J. Stable flocking of mobile agents, Part I:fixed topology. In:Proceedings of the 42nd IEEE Conference on Decision and Control. Maui, HI:IEEE, 2003. 2010-2015
    [17]
    Ren W, Beard R W, Atkins E M. Information consensus in multivehicle cooperative control. IEEE Control Systems Magazine, 2007, 27(2):71-82
    [18]
    Jadbabaie A, Lin J, Morse A. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 2003, 48(6):988-1001
    [19]
    Ghabcheloo R, Aguiar A P, Pascoal A, Silvestre C, Kaminer I, Hespanha J. Coordinated path-following in the presence of communication losses and time delays. SIAM Journal on Control and Optimization, 2009, 48(1):234-265
    [20]
    Xin H H, Qu Z H, Seuss J, Maknouninejad A. A self organizing strategy for power flow control of photovoltaic generators in a distribution network. IEEE Transactions on Power Systems, 2011, 26(3):1462-1473
    [21]
    Krstic M, Kanellakopoulos I, Kokotovic P V. Nonlinear and Adaptive Control Design. New York:John Wiley and Sons, 1995
    [22]
    Siljak D D. Decentralized Control of Complex Systems. Boston:Academic Press, 1991
    [23]
    Sontag E D. Smooth stabilization implies coprime factorization. IEEE Transactions on Automatic Control, 1989, 34(4):435-443
    [24]
    Sontag E D. Input to state stability:basic concepts and results. Nonlinear and Optimal Control Theory. Berlin:Springer-Verlag, 2007. 163-220
    [25]
    Jiang Z P, Teel A R, Praly L. Small-gain theorem for ISS systems and applications. Mathematics of Control, Signals and Systems, 1994, 7(2):95-120
    [26]
    Sontag E D, Wang Y. Notions of input to output stability. Systems and Control Letters, 1999, 38(4-5):235-248
    [27]
    Jiang Z P, Wang Y. A generalization of the nonlinear small-gain theorem for large-scale complex systems. In:Proceedings of the 7th World Congress on Intelligent Control and Automation. Chongqing, China:IEEE, 2008. 1188-1193
    [28]
    Liu T F, Hill D J, Jiang Z P. Lyapunov formulation of ISS cyclic-smallgain in continuous-time dynamical networks. Automatica, 2011, 47(9):2088-2093
    [29]
    Karafyllis I, Jiang Z P. Stability and Stabilization of Nonlinear Systems. London:Springer, 2011
    [30]
    Jiang Z P, Mareels I M Y, Wang Y. A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems. Automatica, 1996, 32(8):1211-1214
    [31]
    Liu T F, Jiang Z P, Hill D J. Decentralized output-feedback control of large-scale nonlinear systems with sensor noise. Automatica, 2012, 48(10):2560-2568
    [32]
    Liu T, Jiang Z P. Distributed output-feedback control of nonlinear multiagent systems. IEEE Transactions on Automatic Control, 2013, 58(11):2912-2917
    [33]
    Jiang Z P, Repperger D W, Hill D J. Decentralized nonlinear outputfeedback stabilization with disturbance attenuation. IEEE Transactions on Automatic Control, 2001, 46(10):1623-1629
    [34]
    Liu T F, Jiang Z P. Distributed formation control of nonholonomic mobile robots without global position measurements. Automatica, 2013, 49(2):592-600
    [35]
    Khalil H K. Nonlinear Systems (3rd Edition). New Jersey:Prentice-Hall, 2002
    [36]
    Tiwari S, Wang Y, Jiang Z P. A nonlinear small-gain theorems for large-scale time-delay systems. Dynamics of Continuous, Discrete and Impulsive Systems Series A:Mathematical Analysis, 2012, 19:27-63
    [37]
    Jiang Z P, Mareels I M Y. A small-gain control method for nonlinear cascade systems with dynamic uncertainties. IEEE Transactions on Automatic Control, 1997, 42(3):292-308
    [38]
    Praly L, Wang Y. Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability. Mathematics of Control, Signals and Systems, 1996, 9(1):1-33

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 (1092) PDF downloads(6) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return