Advertisement

Science China Technological Sciences

, Volume 62, Issue 4, pp 665–676 | Cite as

Affine formation maneuver tracking control of multiple second-order agents with time-varying delays

  • Yang Xu
  • DongYu Li
  • DeLin LuoEmail author
  • YanCheng You
Article
  • 9 Downloads

Abstract

This paper considers an affine maneuver tracking control problem for leader-follower type second-order multi-agent systems in the presence of time-varying delays, where the interaction topology is directed. Using the property of the affine transformation, this paper gives the sufficient and necessary conditions of achieving the affine localizability and extends it to the second-order condition. Under the (n + 1)-reachable condition of the given n-dimensional nominal formation with n + 1 leaders, a formation of agents can be reshaped in arbitrary dimension by only controlling these leaders. When the neighboring positions and velocities are available, a formation maneuver tracking control protocol with time-varying delays is constructed with the form of linear systems, where the tracking errors of the followers can be specified. Based on Lyapunov-Krasovskii stability theory, sufficient conditions to realize affine maneuvers are proposed and proved, and the unknown control gain matrix can be solved only by four linear matrix inequalities independent of the number of agents. Finally, corresponding simulations are carried out to verify the theoretical results, which show that these followers can track the time-varying references accurately and continuously.

Keywords

formation control affine transformation multi-agent systems second-order dynamics time-varying delays 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ren W, Beard RW. Consensus seeking in multiagent systems under dy-namically changing interaction topologies. IEEE Trans Automat Contr, 2005, 50: 655–661CrossRefzbMATHGoogle Scholar
  2. 2.
    Ren W, Beard RW, Atkins E M. Information consensus in multivehicle cooperative control. IEEE Control Syst, 2007, 27: 71–82CrossRefGoogle Scholar
  3. 3.
    Ren W. Multi-vehicle consensus with a time-varying reference state. Syst Control Lett, 2007, 56: 474–483MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ren W, Beard R W. Consensus algorithms for double-integrator dy-namics. In: Distributed Consensus in Multi-vehicle Cooperative Con-trol: Theory and Applications. London: Springer, 2008CrossRefGoogle Scholar
  5. 5.
    Chen Y, Lu J H, Yu X H. Robust consensus of multi-agent systems with time-varying delays in noisy environment. Sci China Tech Sci, 2011, 54: 2014–2023Google Scholar
  6. 6.
    Liu K X, Wu L L, L¨u J H, et al. Finite-time adaptive consensus of a class of multi-agent systems. Sci China Tech Sci, 2016, 59: 22–32CrossRefGoogle Scholar
  7. 7.
    Cao Y, Stuart D, Ren W, et al. Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: Algo-rithms and experiments. IEEE Trans Contr Syst Technol, 2011, 19: 929–938CrossRefGoogle Scholar
  8. 8.
    Cao Y, Ren W, Egerstedt M. Distributed containment control with mul-tiple stationary or dynamic leaders in fixed and switching directed net-works. Automatica, 2012, 48: 1586–1597MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Li Z, Ren W, Liu X, et al. Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders. Int J Robust Nonlinear Control, 2013, 23: 534–547MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Li Z, Duan Z, Ren W, et al. Containment control of linear multi-agent systems with multiple leaders of bounded inputs using distributed con-tinuous controllers. Int J Robust Nonlinear Control, 2015, 25: 2101–2121CrossRefzbMATHGoogle Scholar
  11. 11.
    Duan H B, Luo Q N, Yu Y X. Trophallaxis network control approach to formation flight of multiple unmanned aerial vehicles. Sci China Tech Sci, 2013, 56: 1066–1074CrossRefGoogle Scholar
  12. 12.
    Oh K K, Park M C, Ahn H S. A survey of multi-agent formation con-trol. Automatica, 2015, 53: 424–440MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Zheng R, Liu Y, Sun D. Enclosing a target by nonholonomic mobile robots with bearing-only measurements. Automatica, 2015, 53: 400–407MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Dong X, Yu B, Shi Z, et al. Time-varying formation control for un-manned aerial vehicles: Theories and applications. IEEE Trans Contr Syst Technol, 2015, 23: 340–348CrossRefGoogle Scholar
  15. 15.
    Dong X, Zhou Y, Ren Z, et al. Time-varying formation control for un-manned aerial vehicles with switching interaction topologies. Control Eng Practice, 2016, 46: 26–36CrossRefGoogle Scholar
  16. 16.
    Lin Z, Wang L, Han Z, et al. Distributed formation control of multi-agent systems using complex laplacian. IEEE Trans Automat Contr, 2014, 59: 1765–1777MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Han Z, Wang L, Lin Z, et al. Formation control with size scaling via a complex laplacian-based approach. IEEE Trans Cybern, 2016, 46: 2348–2359CrossRefGoogle Scholar
  18. 18.
    Han T, Lin Z, Zheng R, et al. A barycentric coordinate-based approach to formation control under directed and switching sensing graphs. IEEE Trans Cybern, 2018, 48: 1202–1215CrossRefGoogle Scholar
  19. 19.
    Lin Z, Wang L, Chen Z, et al. Necessary and sufficient graphical con-ditions for affine formation control. IEEE Trans Automat Contr, 2016, 61: 2877–2891CrossRefzbMATHGoogle Scholar
  20. 20.
    Zhao S. Affine Formation Maneuver Control of Multiagent Systems. IEEE Trans Automat Contr, 2018, 63: 4140–4155MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Xu Y, Zhao S Y, Luo D L, et al. Affine formation maneuver control of multi-agent systems with directed interaction graphs. In: Proceedings of the 37th Conference on Chinese Control (CCC 2018). Wuhan, 2018. 4563–4568CrossRefGoogle Scholar
  22. 22.
    Li D, Zhang W, He W, et al. Two-Layer Distributed Formation-Containment Control of Multiple Euler-Lagrange Systems by Output Feedback.. IEEE Trans Cybern, 2019, 49: 675–687CrossRefGoogle Scholar
  23. 23.
    Xu Y, Lai S, Li J, et al. Concurrent Optimal Trajectory Planning for Indoor Quadrotor Formation Switching. J Intell Robot Syst, 2018, 20Google Scholar
  24. 24.
    Liu C L, Tian Y P. Formation control of multi-agent systems with het-erogeneous communication delays. Int J Syst Sci, 2009, 40: 627–636CrossRefzbMATHGoogle Scholar
  25. 25.
    Abdessameud A, Tayebi A. Formation control of VTOL Unmanned Aerial Vehicles with communication delays. Automatica, 2011, 47: 2383–2394MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Lu X, Austin F, Chen S. Formation control for second-order multi-agent systems with time-varying delays under directed topology. Com-mun Nonlinear Sci Numer Simul, 2012, 17: 1382–1391MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Li P, Qin K, Pu H. Distributed robust time-varying formation control for multiple unmanned aerial vehicles systems with time-delay. In: Proceedings of the 29th Conference on Chinese Control and Decision (CCDC 2017). Chongqing, 2017. 1539–1544Google Scholar
  28. 28.
    Liu R, Cao X, Liu M. Finite-time synchronization control of spacecraft formation with network-induced communication delay. IEEE Access, 2017, 5: 27242–27253CrossRefGoogle Scholar
  29. 29.
    Han L, Dong X, Li Q, et al. Formation-containment control for second-order multi-agent systems with time-varying delays. Neurocomputing, 2016, 218: 439–447CrossRefGoogle Scholar
  30. 30.
    Ballantine C S. Stabilization by a diagonal matrix. Proc Amer Math Soc, 1970, 25: 728–728MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Xi J, Shi Z, Zhong Y. Consensus analysis and design for high-order linear swarm systems with time-varying delays. Phys A-Stat Mech its Appl, 2011, 390: 4114–4123CrossRefGoogle Scholar
  32. 32.
    Zhang X M, Wu M, She J H, et al. Delay-dependent stabilization of linear systems with time-varying state and input delays. Automatica, 2005, 41: 1405–1412MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Boyd S, El Ghaoui L, Feron E, et al. Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Math-ematics, 1994Google Scholar
  34. 34.
    Dong X, Han L, Li Q, et al. Containment analysis and design for gen-eral linear multi-agent systems with time-varying delays. Neurocom-puting, 2016, 173: 2062–2068CrossRefGoogle Scholar
  35. 35.
    Li Z, Wen G, Duan Z, et al. Designing fully distributed consensus pro-tocols for linear multi-agent systems with directed graphs. IEEE Trans Automat Contr, 2015, 60: 1152–1157CrossRefzbMATHGoogle Scholar
  36. 36.
    Lv Y, Li Z, Duan Z, et al. Distributed adaptive output feedback con-sensus protocols for linear systems on directed graphs with a leader of bounded input. Automatica, 2016, 74: 308–314MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Aerospace EngineeringXiamen UniversityXiamenChina
  2. 2.Department of Electrical and Computer EngineeringNational University of SingaporeSingaporeSingapore
  3. 3.Department of Control Science and EngineeringHarbin Institute of TechnologyHarbinChina

Personalised recommendations