Skip to main content
SpringerLink
Log in

Robust cooperation of connected vehicle systems with eigenvalue-bounded interaction topologies in the presence of uncertain dynamics

  • Research Article
  • Published:
Frontiers of Mechanical Engineering Aims and scope Submit manuscript

Abstract

This study presents a distributed H-infinity control method for uncertain platoons with dimensionally and structurally unknown interaction topologies provided that the associated topological eigenvalues are bounded by a predesigned range.With an inverse model to compensate for nonlinear powertrain dynamics, vehicles in a platoon are modeled by third-order uncertain systems with bounded disturbances. On the basis of the eigenvalue decomposition of topological matrices, we convert the platoon system to a norm-bounded uncertain part and a diagonally structured certain part by applying linear transformation. We then use a common Lyapunov method to design a distributed H-infinity controller. Numerically, two linear matrix inequalities corresponding to the minimum and maximum eigenvalues should be solved. The resulting controller can tolerate interaction topologies with eigenvalues located in a certain range. The proposed method can also ensure robustness performance and disturbance attenuation ability for the closed-loop platoon system. Hardware-in-the-loop tests are performed to validate the effectiveness of our method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zhang J, Wang F, Wang K, et al. Data-driven intelligent transportation systems: A survey. IEEE Transactions on Intelligent Transportation Systems, 2011, 12(4): 1624–1639

    Article  Google Scholar 

  2. Luettel T, Himmelsbach M, Wuensche J. Autonomous ground vehicles—Concepts and a path to the future. Proceedings of the IEEE, 2012, 100(Special Centennial Issue): 1831–1839

    Article  Google Scholar 

  3. Caveney D. Cooperative vehicular safety applications. IEEE Control Systems Magazine, 2010, 30(4): 38–53

    Article  MathSciNet  Google Scholar 

  4. Shladover S, Desoer C, Hedrick J, et al. Automated vehicle control developments in the PATH program. IEEE Transactions on Vehicular Technology, 1991, 40(1): 114–130

    Article  Google Scholar 

  5. Rajamani R, Tan H, Law B, et al. Demonstration of integrated lateral and longitudinal control for the operation of automated vehicles in platoons. IEEE Transactions on Control Systems Technology, 2000, 8(4): 695–708

    Article  Google Scholar 

  6. Swaroop D, Hedrick J K, Chien C C, et al. A comparison of spacing and headway control laws for automatically controlled vehicles. Vehicle System Dynamics, 1994, 23(8): 597–625

    Article  Google Scholar 

  7. Zhou J, Peng H. Range policy of adaptive cruise control vehicle for improved flow stability and string stability. IEEE Transactions on Intelligent Transportation Systems, 2005, 6(2): 229–237

    Article  Google Scholar 

  8. Swaroop D, Hedrick J. Constant spacing strategies for platooning in automated highway systems. Journal of Dynamic Systems, Measurement, and Control, 1999, 121(3): 462–470

    Article  Google Scholar 

  9. Fax A, Murray R. Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control, 2004, 49: 1465–1476

    Article  MathSciNet  MATH  Google Scholar 

  10. Yadlapalli S K, Darbha S, Rajagopal K R. Information flow and its relation to stability of the motion of vehicles in a rigid formation. In: Proceedings of the 2005 American Control Conference. Portland: IEEE, 2006, 1315–1319

    Google Scholar 

  11. Zheng Y, Li S, Wang J, et al. Influence of information flow topology on closed-loop stability of vehicle platoon with rigid formation. In: Proceedings of the 17th International Conference on Intelligent Transportation System. Qingdao: IEEE, 2014, 2094–2100

    Google Scholar 

  12. Xiao L, Cao F. Practical string stability of platoon of adaptive cruise control vehicles. IEEE Transactions on Intelligent Transportation Systems, 2011, 12(4): 1184–1194

    Article  Google Scholar 

  13. Teo R, Stipanovic D, Tomlin C. Decentralized spacing control of a string of multiple vehicles over lossy data links. IEEE Transactions on Control Systems Technology, 2010, 18(2): 469–473

    Article  Google Scholar 

  14. Shaw E, Hedrick J. String stability analysis for heterogeneous vehicle strings. In: Proceedings of the 2007 American Control Conference. New York: IEEE, 2007, 3118–3125

    Chapter  Google Scholar 

  15. Zheng Y, Li S E, Li K, et al. Distributed model predictive control for heterogeneous vehicle platoons under unidirectional topologies. IEEE Transactions on Control Systems Technology, 2017, 25(3): 899–910

    Article  MathSciNet  Google Scholar 

  16. Liang C, Peng H. Optimal adaptive cruise control with guaranteed string stability. Vehicle System Dynamics, 1999, 32(4–5): 313–330

    Article  Google Scholar 

  17. Stankovic S, Stanojevic M, Siljak D. Decentralized overlapping control of a platoon of vehicles. IEEE Transactions on Control Systems Technology, 2000, 8(5): 816–831

    Article  Google Scholar 

  18. Dunbar W, Caveney D. Distributed receding horizon control of vehicle platoons: Stability and string stability. IEEE Transactions on Automatic Control, 2012, 57(3): 620–633

    Article  MathSciNet  MATH  Google Scholar 

  19. Zheng Y, Li S E, Li K, et al. Stability margin improvement of vehicular platoon considering undirected topology and asymmetric control. IEEE Transactions on Control Systems Technology, 2016, 24(4): 1253–1265

    Article  MathSciNet  Google Scholar 

  20. Kianfar R, Augusto B, Ebadighajari A, et al. Design and experimental validation of a cooperative driving system in the grand cooperative driving challenge. IEEE Transactions on Intelligent Transportation Systems, 2012, 13(3): 994–1007

    Article  Google Scholar 

  21. Chan E, Gilhead P, Jelinek P, et al. Cooperative control of SARTRE automated platoon vehicles. In: Proceedings of the 19th ITS World Congress. Vienna, 2012, 1–9

    Google Scholar 

  22. Tsugawa S, Kato S, Aoki K. An automated truck platoon for energy saving. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. San Francisco: IEEE, 2011, 32(14): 4109–4114

    Google Scholar 

  23. Zheng Y, Li S, Wang J, et al. Stability and scalability of homogeneous vehicular platoon: Study on the influence of information flow topologies. IEEE Transactions on Intelligent Transportation Systems, 2016, 17(1): 14–26

    Article  Google Scholar 

  24. Willke T, Tientrakool P, Maxemchuk N F. A survey of inter-vehicle communication protocols and their applications. IEEE Communications Surveys & Tutorials, 2009, 11(2): 3–20

    Article  Google Scholar 

  25. Ploeg J, Serrarens A, Heijenk G. Connect & drive: Design and evaluation of cooperative adaptive cruise control for congestion reduction. Journal of Modern Transportation, 2011, 19(3): 207–213

    Article  Google Scholar 

  26. Guo G, Yue W. Autonomous platoon control allowing range-limited sensors. IEEE Transactions on Vehicular Technology, 2012, 61(7): 2901–2912

    Article  Google Scholar 

  27. Herman I, Martinec D, Hurak Z, et al. Nonzero bound on Fiedler eigenvalue causes exponential growth of H-infinity norm of vehicular platoon. IEEE Transactions on Automatic Control, 2015, 60(8): 2248–2253

    Article  MathSciNet  MATH  Google Scholar 

  28. Naus G J L, Vugts R P A, Ploeg J, et al. String-stable CACC design and experimental validation: A frequency-domain approach. IEEE Transactions on Vehicular Technology, 2010, 59(9): 4268–4279

    Article  Google Scholar 

  29. Gao F, Li K. Hierarchical switching control of longitudinal acceleration with large uncertainties. International Journal of Automotive Technology, 2007, 8(3): 351–359

    Google Scholar 

  30. Li S, Gao F, Cao D, et al. Multiple model switching control of vehicle longitudinal dynamics for platoon level automation. IEEE Transactions on Vehicular Technology, 2016, 65(6): 4480–4492

    Article  Google Scholar 

  31. Hu G. Robust consensus tracking of a class of second-order multiagent dynamic systems. Systems & Control Letters, 2012, 61(1): 134–142

    Article  MathSciNet  MATH  Google Scholar 

  32. Han D, Chesi G, Hung Y. Robust consensus for a class of uncertain multi-agent dynamical systems. IEEE Transactions on Industrial Informatics, 2013, 9(1): 306–312

    Article  Google Scholar 

  33. Huang W, Zeng J, Sun H. Robust consensus for linear multi-agent systems with mixed uncertainties. Systems & Control Letters, 2015, 76: 56–65

    Article  MathSciNet  MATH  Google Scholar 

  34. Gao F, Li S, Zheng Y, et al. Robust control of heterogeneous vehicular platoon with uncertain dynamics and communication delay. IET Intelligent Transport Systems, 2016, 10(7): 503–513

    Article  Google Scholar 

  35. Gao F, Dang D, Huang S, Li S. Decoupled robust control of vehicular platoon with identical controller and rigid information flow. International Journal of Automotive Technology, 2017, 18(1): 157–164

    Article  Google Scholar 

  36. Ren W, Beard R. Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 2005, 50(5): 655–661

    Article  MathSciNet  MATH  Google Scholar 

  37. Godsil C, Royle G F. Algebraic Graph Theory. Springer Science & Business Media, 2013

    MATH  Google Scholar 

  38. Zheng Y, Li S E, Li K, et al. Platooning of connected vehicles with undirected topologies: Robustness analysis and distributed Hinfinity controller synthesis. IEEE Transactions on Intelligent Transportation Systems, 2016, PP(99): 1–12

    Google Scholar 

  39. Zhang L, Orosz G. Motif-based design for connected vehicle systems in presence of heterogeneous connectivity structures and time delays. IEEE Transactions on Intelligent Transportation Systems, 2016, 17(6): 1638–1651

    Article  Google Scholar 

  40. Gao F, Li S, Kum D, et al. Synthesis of multiple model switching controllers using H-infinity theory for systems with large uncertainties. NeuroComputing, 2015, 157: 118–124

    Article  Google Scholar 

  41. Gao F, Dang D, Li S, et al. Control of large model mismatch system using multiple models. International Journal of Control Automation and Systems, 2017, 15(4): 1494–1506

    Article  Google Scholar 

Download references

Acknowledgements

This study was supported by the NSF China (Grant Nos. 51575293 and 51622504), National Key R&D Program of China (Grant No. 2016YFB0100906), International Sci&Tech Cooperation Program of China (Grant No. 2016YFE0102200), and the Open Fund of State Key Lab of Automotive Safety and Energy (Grant No. KF16192). Special gratitude is extended to Prof. R. Rajamani of the University of Minnesota and Prof. G. Orosz of the University of Michigan for their invaluable comments and suggestions.

Author information

Authors and Affiliations

  1. State Key Laboratory of Automotive Safety and Energy, Department of Automotive Engineering, Tsinghua University, Beijing, 100084, China

    Keqiang Li, Shengbo Eben Li & Hongbo Gao

  2. School of Automotive Engineering, Chongqing University, Chongqing, 400044, China

    Feng Gao

  3. Department of Engineering Science, University of Oxford, Oxford, OX13PJ, UK

    Yang Zheng

Authors
  1. Keqiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shengbo Eben Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yang Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hongbo Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Feng Gao or Shengbo Eben Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, K., Gao, F., Li, S.E. et al. Robust cooperation of connected vehicle systems with eigenvalue-bounded interaction topologies in the presence of uncertain dynamics. Front. Mech. Eng. 13, 354–367 (2018). https://doi.org/10.1007/s11465-018-0486-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11465-018-0486-x

Keywords

Search

Navigation