基于自由权矩阵的时变时延线性群系统编队控制

doi:10.7527/S1000-6893.2017.21628

电子电气工程与控制

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基于自由权矩阵的时变时延线性群系统编队控制

石晓航¹, 张庆杰², 吕俊伟¹

1. 海军航空大学控制工程系, 烟台 264001;
2. 空军航空大学飞行器控制系, 长春 130022

收稿日期:2017-07-25 修回日期:2017-11-03 出版日期:2018-03-15 发布日期:2017-11-03
通讯作者: 吕俊伟,E-mail:lvjw369@163.com E-mail:lvjw369@163.com
基金资助:
国家自然科学基金（61004002）；航空科学基金（20155884012）

Formation control for linear swarm systems with time-varying delays based on free-weighting matrices

SHI Xiaohang¹, ZHANG Qingjie², LYU Junwei¹

1. Department of Control Engineering, Naval Aeronautical University, Yantai 264001, China;
2. Department of Aircraft Control, Aviation University of Air Force, Changchun 130022, China

Received:2017-07-25 Revised:2017-11-03 Online:2018-03-15 Published:2017-11-03
Supported by:
National Natural Science of China (61004002); Aeronautical Science Foundation of China (20155884012)

摘要/Abstract

摘要： 研究了基于自由权矩阵方法的时变时延线性群系统编队控制问题。首先，基于一致性理论，设计了具有时变时延的线性群系统编队控制协议。其次，通过变量代换，将时延条件下的线性群系统编队控制问题转化为时延系统的镇定问题。构造Lyapunov-Krasovskii函数，并利用自由权矩阵方法对时延系统的镇定问题进行分析，得到了保守性较小的线性矩阵不等式（LMI）判据，并求解出时延上界和编队控制器增益。最后，通过仿真实验，验证了方法的有效性。

关键词: 群系统, 一致性, 编队控制, 自由权矩阵, 时变时延

Abstract: Based on free-weighting matrices method, the formation control for the linear swarm systems with time-varying delays is investigated. First, a protocol for the formation control with time-varying delays is proposed based on consensus theory. Second, the formation control problem is transformed into the stabilization problem of delay-dependent system using variable substitution. The Lyapunov-Krasovskii function is constructed, and the stabilization problem of the delay-dependent system is analyzed using free-weighting matrices method. Then, the Linear Matrix Inequality (LMI) criterion with lower conservatism is obtained. The upper bounds of delays and the controller gains are also given. Finally, the effectiveness of the method is verified through the simulation experiments.

Key words: swarm systems, consensus, formation control, free-weighting matrices, time-varying delays

中图分类号:

V249

石晓航, 张庆杰, 吕俊伟. 基于自由权矩阵的时变时延线性群系统编队控制[J]. 航空学报, 2018, 39(3): 321628-321628.

SHI Xiaohang, ZHANG Qingjie, LYU Junwei. Formation control for linear swarm systems with time-varying delays based on free-weighting matrices[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(3): 321628-321628.

参考文献

[1] NIGAM N, BIENIAWSKI S, KROO I, et al. Control of multiple UAVs for persistent surveillance:Algorithm and flight test results[J]. IEEE Transactions on Control Systems Technology, 2012, 20(5):1236-1251.
[2] CHEN Y Q, WANG Z. Formation control:A review and a new consideration[C]//Proceedings of the 2005 IEEE/RSI International Conference on Intelligent Robots and Systems. Piscataway, NJ:IEEE Press, 2005:3181-3186.
[3] WANG P K C. Navigation strategies for multiple autonomous mobile robots moving in formation[J]. Journal of Robotic Systems, 1991, 8(2):177-195.
[4] LEWIS M, TAN K. High precision formation control of mobile robots using virtual structures[J]. Autonomous Robots, 1997, 4(4):387-403.
[5] BALCH T, ARKIN R. Behavior-based formation control for multi-robot teams[J]. IEEE Transactions on Robotics and Automation, 1998, 14(6):926-939.
[6] REZA O S, RICHARD M M. Consensus protocols for networks of dynamic agents[C]//American Control Conference. Piscataway, NJ:IEEE Press, 2003:951-956.
[7] REZA O S, RICHARD M M. Consensus problems in networks of agents with switching topology and time-delays[J]. IEEE Transactions on Automatic Control, 2004, 49(9):1520-1533.
[8] FENG X, LONG W, JIE C, et al. Finite-time formation control for multi-agent systems[J]. Automatic, 2009, 45(11):2605-2611.
[9] REN W. Consensus strategies for cooperative control of vehicle formation[J]. IET Control Theory & Application, 2007, 1(2):505-512.
[10] REN W, SORENSEN N. Distributed coordination architecture for multi-robot formation control[J]. Robotics and Autonomous Systems, 2008, 56(4):324-333.
[11] DONG R S, GENG Z Y. Consensus for formation control of multi-agent systems[J]. International Journal of Robust and Nonlinear Control, 2014, 25(14):2481-2501.
[12] DONG X W, YU B C, SHI Z Y, et al. Time-varying formation control for unmanned aerial vehicles:Theories and applications[J]. IEEE Transactions on Control Systems Technology, 2015, 23(1):340-348.
[13] DONG X W, ZHOU Y, REN Z, et al. Time-varying formation control for unmanned aerial vehicles with switching interaction topologies[J]. Control Engineering Practice, 2016, 46:26-36.
[14] 刘伟, 周绍磊, 祁亚辉, 等. 有向切换通信拓扑下多无人机分布式编队控制[J]. 控制理论与应用, 2015, 32(10):1422-1427. LIU W, ZHOU S L, QI Y H, et al. Distributed formation control for multiple unmanned aerial vehicles with directed switching communication topologies[J]. Control Theory & Applications, 2015, 32(10):1422-1427(in Chinese).
[15] LIN Z Y, FRANCIS B, MAGGIORE M. Necessary and sufficient graphical conditions for formation control of unicycles[J]. IEEE Transactions on Automatic Control, 2005, 50(1):121-127.
[16] FAX J A, MURRAY R M. Information flow and cooperative control of vehicle formations[J]. IEEE Transactions on Automatic Control, 2004, 49(9):1465-1476.
[17] PORFIRI M, ROBERSON D G, STILWELL D J. Tracking and formation control of multiple autonomous agents:A two-level consensus approach[J]. Automatica, 2007, 43(8):1318-1328.
[18] LAFFERRIERE G, WILLIAMS A, CAUGHMAN J, et al. Decentralized control of vehicle formations[J]. Systems and Control Letters, 2005, 54(9):899-910.
[19] MA C Q, ZHANG J F. On formability of linear continuous-time multi-agent systems[J]. Journal of Systems Science and Complexity, 2012, 25(1):13-29.
[20] LIU C L, TIAN Y P. Formation control of multi-agent systems with heterogeneous communication delays[J]. International Journal of Systems Science, 2009, 40(6):627-636.
[21] RUDY C G, NEJAT O. Stability of formation control using a consensus protocol under directed communications with two time delays and delay scheduling[J]. International Journal of Systems Science, 2015, 47(2):433-449.
[22] 薛瑞彬, 宋建梅, 张民强. 具有时延及联合连通拓扑的多飞行器分布式协同编队飞行控制研究[J]. 兵工学报, 2015, 36(3):492-502. XUE R B, SONG J M, ZHANG M Q. Research on distributed multi-vehicle coordinated formation flight control with coupling time-delay and jointly-connected topologies[J]. Acta Armamentarii, 2015, 36(3):492-502(in Chinese).
[23] LU X Q, AUSTIN F, CHEN S H. Formation control for second-order multi-agent systems with time-varying delays under directed topology[J]. Communications in Nonlinear Science and Numerical Simulation, 2012, 17(3):1382-1391.
[24] DONG X W, XI J X, LU G, et al. Formation control for high-order linear time-invariant multi-agent systems with time delays[J]. IEEE Transactions on Control of Network Systems, 2014, 1(3):232-240.
[25] 张庆杰, 沈林成, 朱华勇. 具有多个通信时延的一类二阶多智能体系统平均一致性[J]. 控制与决策, 2011, 26(10):1485-1492 ZHANG Q J, SHEN L C, ZHU H Y. Average consensus of a class of second order multi-agent systems with multiple communication delays[J]. Control and Decision, 2011, 26(10):1485-1492(in Chinese).
[26] ZHANG Q J, NIU Y F, WANG L, et al. Average consensus seeking of high-order continuous-time multi-agent systems with multiple time-varying communication delays[J]. International Journal of Control, Automation and Systems, 2011, 9(6):1209-1218.
[27] HE Y, WU M, SHE J H, et al. Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties[J]. IEEE Transactions on Automatic Control, 2004, 49(5):828——832.
[28] WU M, HE Y, SHE J H, et al. Delay-dependent criteria for robust stability of time-varying delay systems[J]. Automatica, 2004, 40(8):1435-1439.
[29] REN W, BEARD R W. Consensus seeking in multiagent systems under dynamically changing interaction topologies[J]. IEEE Transactions on Automatic Control, 2005, 50(5):655-661.
[30] ZHOU S L, LIU W, WU Q P, et al. Leaderless consensus of linear multi-agent systems:Matrix decomposition approach[C]//Proceedings of the 7th International Conference on Intelligent Human-Machine Systems and Cybernetics. Piscataway, NJ:IEEE Press, 2015:327-331.
[31] BOYD S, GHAOUI L E, FERON E, et al. Linear matrix inequalities in system and control theory[M]. Philadelphia, PA:SIAM, 1994:7-8.
[32] GU K. A further refinement of discretized Lyapunov functional method for the stability of time-delay systems[J]. International Journal of Control, 2001, 74(10):967-976.
[33] 周绍磊, 祁亚辉, 张雷, 等. 切换拓扑下无人机集群系统时变编队控制[J]. 航空学报, 2017, 38(4):320452. ZHOU S L, QI Y H, ZHANG L, et al. Time-varying formation control of UAV swarm systems with switching topologies[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(4):320452(in Chinese).

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基于自由权矩阵的时变时延线性群系统编队控制

Formation control for linear swarm systems with time-varying delays based on free-weighting matrices

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