Second-order consensus for directed multi-agent systems with sampled data
Qian Ma
School of Automation, Nanjing University of Science and Technology, Nanjing, 210094 China
Search for more papers by this authorCorresponding Author
Shengyuan Xu
School of Automation, Nanjing University of Science and Technology, Nanjing, 210094 China
Correspondence to: Shengyuan Xu, School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China.
E-mail: [email protected]
Search for more papers by this authorFrank L. Lewis
Automation and Robotics Research Institute, The University of Texas at Arlington, TX, 76118 USA
Search for more papers by this authorQian Ma
School of Automation, Nanjing University of Science and Technology, Nanjing, 210094 China
Search for more papers by this authorCorresponding Author
Shengyuan Xu
School of Automation, Nanjing University of Science and Technology, Nanjing, 210094 China
Correspondence to: Shengyuan Xu, School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China.
E-mail: [email protected]
Search for more papers by this authorFrank L. Lewis
Automation and Robotics Research Institute, The University of Texas at Arlington, TX, 76118 USA
Search for more papers by this authorSUMMARY
This paper deals with the consensus problem of second-order multi-agent systems with sampled data. Because of the unavailable velocity information, consensus problem is studied only by using the sampled position information. The final consensus states of multi-agent system are given. And a necessary and sufficient consensus condition is provided, which depends on the parameters of sampling interval, eigenvalues of Laplacian matrix, and coupling strengths. Then, the case that both the sampled position and velocity information can be obtained is discussed. On the basis of introducing a time-varying piecewise-continuous delay and proposing a novel time-dependent Lyapunov functional, the sufficient consensus condition is presented, and the upper bound of sampling interval can be estimated. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. Copyright © 2013 John Wiley & Sons, Ltd.
REFERENCES
- 1 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.
- 2 Vicsek T, Czirok A, Jacob EB, Cohen I, Shochet O. Novel type of phase transition in a system of self-driven particles. Physical Review Letters 1995; 75(6): 1226–1229.
- 3 Saber RO, Murray RM. Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control 2004; 49(9): 1520–1533.
- 4 Ren W, Beard RW. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control 2005; 50(5): 655–661.
- 5 Ren W, Atkins E. Distributed multi-vehicle coordinated control via local information exchange. International Journal of Robust and Nonlinear Control 2007; 17(10): 1002–1033.
- 6 Yu W, Chen G, Cao M. Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. Automatica 2010; 46(6): 1089–1095.
- 7 Hong Y, Chen G, Bushnell L. Distributed observers design for leader-following control of multi-agent networks. Automatica 2008; 44(3): 846–850.
- 8 Ren W. On consensus algorithms for double-integrator dynamics. IEEE Transactions on Automatic Control 2008; 58(6): 1503–1509.
- 9 Liu Y, Jia Y. Consensus problem of high-order multi-agent systems with external disturbances. International Journal of Robust and Nonlinear Control 2010; 20(14): 1579–1593.
- 10 Kim H, Shim H, Seo JH. Output consensus of heterogeneous uncertain linear multi-agent systems. IEEE Transactions on Automatic Control 2011; 56(1): 200–206.
- 11 Li JZ, Ren W, Xu SY. Distributed containment control with multiple dynamic leaders for double-integrator dynamics using only position measurements. IEEE Transactions on Automatic Control 2012; 57(6): 1553–1559.
- 12 Liu H, Xie G, Wang L. Containment of linear multi-agent systems under general interaction topologies. Systems & Control Letters 2012; 61(4): 528–534.
- 13 Meng Z, Ren W, Zheng Y. Distributed finite-time attitude containment control for multiple rigid bodies. Automatica 2010; 46(12): 2092–2099.
- 14 Lin P, Jia Y, Li L. Distributed robust H ∞ consensus control in directed networks of agents with time-delay. Systems & Control Letters 2008; 57: 643–653.
- 15 Lin P, Jia Y. Average consensus in networks of multi-agents with both switching topology and coupling time-delay. Physica A 2008; 387: 303–313.
- 16 Sun Y, Wang L, Xie G. Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays. Systems & Control Letters 2008; 57: 175–183.
- 17 Cao Y, Ren W, Chen Y. Multi-agent consensus using both current and outdated states. Preceedings of the 17th world congress IFAC, Seoul, Korea, 2008; 2874–2879.
- 18 Zhang Y, Tian YP. Consentability and protocol design of multi-agent systems with stochastic switching topology. Automatica 2009; 45(5): 1195–1201.
- 19 Zhao H, Ren W, Yuan D, Chen J. Distributed discrete-time coordinated tracking with Markovian switching topologies. Systems & Control Letters 2012; 61(7): 766–772.
- 20 Porfiri M, Stilwell DJ. Consensus seeking over random weighted directed graphs. IEEE Transactions on Automatic Control 2007; 52(9): 1767–1773.
- 21 Hong Y, Gao L, Cheng D, Hu J. Lyapunov-based approach to multiagent systems with switching jointly connected interconnection. IEEE Transactions on Automatic Control 2007; 52(5): 943–948.
- 22 Qin J, Gao H, Zheng WX. Second-order consensus for multi-agent systems with switching topology and communication delay. Systems & Control Letters 2011; 60(6): 390–397.
- 23 Lin P, Jia Y. Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies. Automatica 2009; 45(9): 2154–2158.
- 24 Liu H, Xie G, Wang L. Necessary and suficient conditions for solving consensus problems of double-integrator dynamics via sampled control. International Journal of Robust and Nonlinear Control 2010; 20(15): 1706–1722.
- 25 Xie G, Liu H, Wang L, Jia Y. Consensus in networked multi-agent systems via sampled control: fixed topology case. Preceedings of 2009 American Control Conference, St. Louis, Missouri, 2009; 3902–3907.
- 26 Ren W, Cao Y. Convergence of sampled-data consensus algorithms for double-integrator dynamics. Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, 2008; 3965–3970.
- 27 Cao Y, Ren W. Multi-vehicle coordination for double-integrator dynamics under fixed undirected/directed interaction in a sampled-data setting. International Journal of Robust and Nonlinear Control 2010; 20(9): 987–1000.
- 28 Cao Y, Ren W. Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction. International Journal of Control 2010; 83(3): 506–515.
- 29 Qin J, Gao H, Zheng WX. Consensus strategy for a class of multi-agents with discrete second-order dynamics. International Journal of Robust and Nonlinear Control 2012; 22(4): 437–452.
- 30 Gao Y, Wang L. Asynchronous consensus of continuous-time multi-agent systems with intermittent measurements. International Journal of Control 2009; 83(3): 552–562.
- 31 Gao Y, Wang L. Consensus of multiple double-integrator agents with intermittent measurement. International Journal of Robust and Nonlinear Control 2010; 20: 1140–1155.
- 32 Gao Y, Wang L. Sampled-data based consensus of continuous-time multi-Agent systems with time-varying topology. IEEE Transactions on Automatic Control 2011; 56(5): 1226–1231.
- 33 Yu W, Zheng W, Chen G, Ren W, Cao J. Second-order consensus in multi-agnet dynamical systems with sampled position data. Automatica 2011; 47(7): 1496–1053.
- 34 Gao Y, Wang L. Consensus of multiple dynamic agents with sampled information. IET Control Theory and Applications 2009; 4(6): 945–956.
- 35 Gao Y, Wang L, Xie G, Wu B. Consensus of multi-agent systems based on sampled-data control. International Journal of Control 2009; 82(12): 2193–2205.
- 36 Gantmacher FR. Applications of the Theory of Matrices. Interscience: New York, 1959.
- 37 Liu K, Fridman E. Wirtinger's inequality and Lyapunov-based sampled-data stabilization. Automatica 2012; 48(1): 102–108.
- 38 Liu KE, Xie G, Wang L. Consensus of multi-agnet systems under double integrator dynamics with time-varying communication delays. International Journal of Robust and Nonlinear Control 2012; 22(17): 1881–1898.
- 39 Gu K. An integral inequality in the stability problem of time-delay systems. Preceedings of 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000; 2805–2810.
