Paper:

# A Survey of Recent Progress in the Study of Distributed High-Order Linear Multi-Agent Coordination

## Jie Huang^{*,**}, Hao Fang^{*}, Jie Chen^{*},

Lihua Dou^{*}, and Jie Zeng^{*}

^{*}School of Automation, Beijing Institute of Technology, Key Laboratory of Intelligent Control and Decision of Complex Systems, Beijing, 100081, China

^{**}Fujian Institute of Education, Fuzhou, 350001, China

Most previous studies ofmulti-agent systems only considered the first- and second-order dynamics. In this review, we present the major results and progress related to distributed high-order linear multi-agent coordination. We also discuss the current challenges and propose several promising research directions, as well as open problems that demand further investigation.

Lihua Dou, and Jie Zeng, “A Survey of Recent Progress in the Study of Distributed High-Order Linear Multi-Agent Coordination,”

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.18, No.1, pp. 83-92, 2014.

- [1] C. Reynolds, “Flocks, herds, and schools: A distributed behavioral model,” Computer Graphics, Vol.21, No.4, pp. 25-34, 1987.
- [2] T. Vicsek, A. Czirk, E. B. Jacob, I. Cohen, and O. Shochet, “Novel type of phase transition in a system of self-driven particles,” Physical Review Letters, Vol.75, No.6, pp. 1226-1229, 1995.
- [3] N. A. Lynch, “Distributed Algorithms,” San Francisco, CA: Morgan Kaufmann, 1996.
- [4] T. Balch and R. C. Arkin, “Behavior-based formation control for multirobot teams,” IEEE Trans. on Robotics and Automation, Vol.14, No.6, pp. 926-939, 1998.
- [5] R. W. Beard, T. W. McLain, M. Goodrich, and E. P. Anderson, “Coordinated target assignment and intercept for unmanned air vehicles,” IEEE Trans. on Robotics and Automation, Vol.18, No.6, pp. 911-922, 2002.
- [6] N. E. Leonard and E. Fiorelli, “Virtual leaders, artificial potentials and coordinated control of groups,” Proc. of the 40th IEEE Conf. on Decision and Control. Orlando, FL, USA: IEEE, pp. 2968-2973, 2001.
- [7] J. T. Feddema, C. Lewis, and D. A. Schoenwald, “Decentralized control of cooperative robotic vehicles: Theory and application,” IEEE Trans. on Robotics and Automation, Vol.18, No.5, pp. 852-864, 2002.
- [8] C. Belta and V. Kumar, “Abstraction and control for groups of robots,” IEEE Trans. on Robotics and Automation, Vol.20, No.5, pp. 865-875, 2004.
- [9] F. Fahimi, “Sliding-mode formation control for underactuated surface vessels,” IEEE Trans. on Robotics, Vol.23, No.3, pp. 617-622, 2007.
- [10] R. Olfati-Saber, R. M. Murray, “Distributed cooperative control of multiple vehicle formations using structural potential functions,” Proc. of the 50th IFAC World Congress. Barcelona, Spain: Int. Federation of Automatic Control, pp. 346-352, 2002.
- [11] X. H. Wang, V. Yadav, and S. N. Balakrishnan, “Cooperative UAV formation flying with obstacle/collision avoidance,” IEEE Trans. on Control Systems Technology, Vo.15, No.4, pp. 672-679, 2007.
- [12] D. J. Stilwell, B. E. Bishop, “Platoons of underwater vehicles,” IEEE Control Systems Magazine, Vol.20, No.6, pp. 45-52, 2000.
- [13] R. Olfati-Saber and J. S. Shamma, “Consensus filters for sensor networks and distributed sensor fusion,” Proc. of the 44th IEEE Conf. on Decision and Control, and the European Control Conf., Seville, Spain: IEEE, pp. 6698-6703, 2005.
- [14] J. Cortés, “Distributed algorithms for reaching consensus on general functions,” Automatica, Vol.44, No.3, pp. 726-737, 2008.
- [15] D. J. Stilwell, B. E. Bishop, “Platoons of underwater vehicles,” IEEE Control Systems Magazine, Vol.20, No.6, pp. 45-52, Dec 2000.
- [16] R. W. Beard, J. Lawton, and F. Y. Hadaegh, “A coordination architecture for spacecraft formation control,” IEEE Trans. on Control Systems Technology, Vol.9, No.6, pp. 777-790, 2001.
- [17] J. R. Lawton and R. W. Beard, “Synchronized multiple spacecraft rotations,” Automatica, Vol.38, No.8, pp. 1359-1364, 2002.
- [18] W. Ren, R. W. Beard, and E. M. Atkins, “Information consensus in multivehicle cooperative control,” IEEE Trans. on Control Systems Technology, Vol.27, No.2, pp. 71-82, 2007.
- [19] R. M. Murray, “Recent research in cooperative control of multivehicle systems,” J. of Dynamic Systems, Measurement, and Control, Vol.129, No.5, pp. 571-583, 2007.
- [20] R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and cooperation in networked multi-agent systems,” Proc. of the IEEE. Vol.95, No.1, pp. 215-233, 2007.
- [21] P. Y. Chebotarev and R. P. Agaev, “Coordination in multiagent systems and Laplacian spectra of digraphs,” Automation and Remote Control, Vol.70, No.3, pp. 469-483, 2009.
- [22] Y. Cao, W. Yu, W. Ren, and G. Chen, “An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination,” IEEE Trans. on Industrial Informatics, Vol.9, No.1, pp. 427-438, 2013.
- [23] H. Min, Y. Liu, S. Wang, and F. Sun, “An Overview on Coordination Control Problem of Multi-agent System,” ACTA Automatica Sinica, Vol.38, No.10, pp. 1557-1570, 2012.
- [24] C. W. Wu, “Synchronization in Complex Networks of Nonlinear Dynamical Systems,” Singapore: World Scientific, 2007.
- [25] J. S. Shamma (Ed.), “Cooperative Control of Distributed Multi-Agent Systems,” Hoboken, NJ: John Wiley & Sons, 2008.
- [26] W. Ren and R. W. Beard, “Distributed Consensus in Multi-vehicle Cooperative Control: Theory and Applications,” London, U.K.: Springer-Verlag, 2008.
- [27] F. Bullo, J. Cortés, and S.Martínez, “Distributed Control of Robotic Networks: a Mathematical Approach to Motion Coordination Algorithms,” Princeton, NJ: Princeton University Press, 2009.
- [28] Z. Qu, “Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles,” London, U.K.: Springer-Verlag, 2009.
- [29] W. Ren and Y. Cao, “Distributed Coordination of Multi-Agent Networks: Emergent Problems, Models, and Issues,” London, U.K.: Springer-Verlag, 2011.
- [30] H. Bai, M. Arcak, and J.Wen, “Cooperative Control Design: A Systematic, Passivity-Based Approach,” New York: Springer-Verlag, 2011.
- [31] M. Maleković and M. Ćubrilo , “Incorporating infatuation in Multi-Agent Systems,” J. of advanced Computational Intelligence and Intelligent Informatics, Vol.10, No.4, pp. 517-521, 2006.
- [32] R. Brena and H. G. Ceballos, “Combining local and global access to ontologies in a multiagent system,” J. of advanced Computational Intelligence and Intelligent Informatics, Vol.9, No.1, pp. 5-12, 2005.
- [33] H. K. Khalil, “Nolinear Systems (Third edition),” Upper Saddle River, NJ, USA: Prentice Hall, 2002.
- [34] W. Ren, K. Moore, Y. Q. Chen, “High-order consensus algorithms in cooperative vehicle systems,” Proc. of the 2006 IEEE Int. Conf. on Networking, Sensing and Control, Ft. Lauderdale, FL, USA: IEEE, pp. 457-462, 2006.
- [35] M. Mesbahi and M. Egerstedt, “Graph Theoretic Methods for Multiagent Networks,” Princeton, NJ, USA: Princeton University Press, 2010.
- [36] W. Ren, K. L. Moore, and Y. Q. Chen, “High-order and model reference consensus algorithms in cooperative control of multivehicle systems,” ASME J. of Dynamic Systems, Measurement, and Control, Vol.129, No.5, pp. 678-688, 2007.
- [37] F. C. Jiang and L.Wang, “Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies,” Int. J. of Control, Vol.83, No.2, pp. 404-420, 2010.
- [38] T. Yang, Y. H. Jin, W. Wang, and Y. J. Shi, “Consensus of highorder continuous-time multi-agent systems with time-delays and switching topologies,” Chinese Physics B, Vol.20, No.2, 0205111-0205116, 2010.
- [39] W. Zhang, D. Zeng, and S. Qu, “Dynamic feedback consensus control of a class of high-order multi-agent systems,” IET Control Theory & Applications, Vol.4, pp. 2219-2222, 2010.
- [40] W. He and J. Cao, “Consensus control for high-order multi-agent systems,” IET Control Theory& Applications, Vol.5, No.1, pp. 231-238, 2011.
- [41] G. Miao, S. Xun, and Y. Zou, “Consentability for high-order multiagent systems under noise environment and timedelays,” J. of the Franklin Institute,Vol.350, pp. 244-257, 2013.
- [42] J. Huang, H. Fang, J. Chen, L. H. Dou, and Q. K. Yang, “On consensus of multiple high-order uncertain nonlinear systems,” Proc. of the 32nd Chinese Control Conf., Xi’an, China, pp. 7145-7149, 2013.
- [43] L. Mo, Y. M. Jia, “
*H*_{∞}Consensus control of a class of high-order multi-agent systems,” IET Control Theory & Applications, Vol.5, No.1, pp. 247-253, 2011. - [44] P. Lin, Y. M. Jia, and L. Li, “Distributed robust
*H*_{∞}consensus control in directed networks of agents with time-delay,” Systems & Control Letters, Vol.57, No.8, pp. 643-653, 2008. - [45] P. Lin, and Y. M. Jia, “Robust
*H*_{∞}consensus analysis of a class of second-order multi-agent systems with uncertainty,” IET Control Theory & Applications, Vol.4, No.3, pp. 487-498, 2010. - [46] Y. Liu and Y.M. Jia, “Consensus problem of high-order multi-agent systems with external disturbances: An
*H*_{∞}analysis approach,” Int. J. of Robust and Nonlinear Control, Vol.20, No.14, pp. 1579-1593, 2010. - [47] F. Zhang and N. E. Leonard, “Cooperative filters and control for cooperative exploration,” IEEE Trans. Autom. Control, Vol.55, No.3, pp. 650-663, 2010.
- [48] P. Lin, Z. Li, Y. M. Jia, and M. Sun, “High-order multi-agent consensus with dynamically changing topologies and time-delays,” IET Control Theory & Applications, Vol.5, No.8, pp. 976-981, 2011.
- [49] X. L.Xu, S. Y. Chen,W.Huang, and L. X. Gao, “Leader-following consensus of discrete-time multi-agent systems with observer-based protocols,” Neurocomputing, Vol.118, pp. 334-341, 2013.
- [50] S. E. Tuna, “Synchronizing linear systems via partial-state coupling,” Automatica, Vol.44, No.8, pp. 2179-2184, 2008.
- [51] L. Scardovi and R. Sepulchre, “Synchronization in networks of identical linear systems,” Automatica, Vol.25, No.11, pp. 2557-2562, 2009.
- [52] S. E. Tuna, “Conditions for synchronizability in arrays of coupled linear systems,” IEEE Trans. on Automatic Control, Vol.54, No.10, pp. 2416-2420, 2009.
- [53] J. H. Seo, H. Shima, and J. Back, “Consensus of high-order linear systems using dynamic output feedback compensator: Low gain approach,” Automatica, Vol.45, No.11, pp. 2659-2664, 2009.
- [54] Z. Li, X. Liu, P. Lin, and W. Ren, “Consensus of linear multi-agent systems with reduced-order observer-based protocols,” Systems & Control Letters, Vol.60, No.7, pp. 510-516, 2011.
- [55] J. Xi, N. Cai, and Y. Zhong, “Consensus problems for high-order linear time-invariant swarm systems,” Physica A: Statistical Mechanics and its Applications, Vol.389, No.24, pp. 5619-5627, 2010.
- [56] N. Cai, J. Xi, and Y. Zhong, “Swarm stability of high-order linear time-invariant swarm systems,” IET Control Theory & Applications, 2011, Vol.5, No.2, pp. 402-408, 2011.
- [57] J. Xi, Z. Shi, and Y. Zhong, “Consensus analysis and design for high-order linear swarm systems with time-varying delays,” Physica A: Statistical Mechanics and its Applications, Vol.390, No.23, pp. 4114-4123, 2011.
- [58] P. Wieland, J. S. Kim, F. Allgöwer, “On topology and dynamics of consensus among linear high-order agents,” Int. J. of Systems Science, Vol.42, No.10, pp. 1831-1842, 2011.
- [59] F. C. Jiang and L.Wang, “Consensus seeking of high-order dynamic multi-agent systems with fixed and swithching topologies,” Int. J. of Control, Vol.83, No.2, pp. 404-420, 2010.
- [60] L. Zeng and G. D. Hu, “Consensus of Linear Multi-Agent Systems with Communication and Input Delays,” Acta Automatica Sinica, Vol.39, No.7, pp. 1133-1140, 2013.
- [61] Y. T. Tang and Y. G. Hong, “Hierarchical Distributed Control Design forMulti-agent Systems Using Approximate Simulation,” Acta Automatica Sinica, Vol.39, No.6, pp. 868-874, 2013.
- [62] J. Wang, Z. Liu, and X. Hu, “Consensus of high order linear multiagent systems using output error feedback,” Proc. of 48th IEEE Conf. on Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conf., Shanghai, China: IEEE, pp. 3685-3690, 2009.
- [63] W. J. Ren, R. W. Beard, and E. M. Atkins, “Information consensus in multivehicle cooperative control,” IEEE Control Systems Magazine, Vol.27, No.2, pp. 71-82, 2007.
- [64] W. J. Dong, “Adaptive consensus seeking of multiple nonlinear systems,” Int. J. of Adaptive Control and Signal Processing, Vol.26, No.5, pp. 419-434, 2012.
- [65] H. Zhang, F. L. Lewis, “Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics,” Automatica, Vol.48, No.7, pp. 1432-1439, 2012.