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

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.

Key words： automated vehicles; platoon; distributed control; robustness

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.

References

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

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

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

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

5 Rajamani R, Tan H, Law B, . 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

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

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

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

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

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

11 Zheng Y, Li S, Wang J, . 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

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

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

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

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

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

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

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

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

20 Kianfar R, Augusto B, Ebadighajari A, . 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

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

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

23 Zheng Y, Li S, Wang J, . 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

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

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

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

27 Herman I, Martinec D, Hurak Z, . 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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