Stability Analysis of a Predecessor-Following Platoon of Vehicles With Two Time Delays
Abstract
The problem of controlling a platoon of vehicles moving in one dimension is considered so that they all follow a lead vehicle with constant spacing between successive vehicles. The stability and the string stability of a platoon of vehicles with two independent and uncertain delays, one in the inter-vehicle distance and the other in the relative velocity information channels, are considered. The main objectives of this paper are: (1) using a simplifying factorization procedure and deploying the cluster treatment of characteristic roots (CTCR) paradigm to obtain exact stability boundaries in the domain of the delays, and (2) for the purpose of disturbance attenuation, the string stability analysis is examined. Finally, a simulation example of multiple vehicle platoon control is used to demonstrate the effectiveness of the proposed method.References
Ghasemi A, Kazemi R, Azadi Sh. Stable decentralized control of platoon of vehicles with heterogeneous information feedback. IEEE Transactions on Vehicular Technology. 2013;62(7):4299-4308.
Hao H, Barooah P. Control of large 1D networks of double integrator agents: role of heterogeneity and asymmetry on stability margin. 2011 Aug: http://arxiv.org/abs/1011.0791v2
Tangerman FM, Veerman JJP, Stosic BD. Asymmetric decentralized flocks. IEEE Transactions on Automatic Control. 2012;57(11):2844-2853.
Guo G, Yue W. Hierarchical platoon control with heterogeneous information feedback. IET Control Theory Appl. 2011;5(15):1766-1781.
Dunbar WB, Caveney D.S. Distributed receding horizon control of vehicle platoons: stability and string stability. IEEE Transactions on Automatic Control. 2012;57(3):620-633.
Xiao L, Gao F. Practical string stability of platoon of adaptive cruise control vehicles. IEEE Transactions on intelligent transportation systems. 2011;12(4):2844-2853.
Middleton R, Braslavsky J. String instability in classes of linear time invariant formation control with limited communication range. IEEE Transactions on Automatic Control. 2010;55(7):1519-1530.
Ghasemi A, Kazemi R, Azadi Sh. Stability analysis of longitudinal control of a platoon of vehicles by considering lags subject to communication delay. The International Journal of Innovative Computing, Information and Control. 2014;10(5):1625-1641.
Yue W, Guo G. Guaranteed cost adaptive control of nonlinear platoons with actuator delay. ASME Journal of Dynamic System Measurement and Control. 2012;134(5):1-11.
Ghasemi A, Kazemi R, Azadi Sh. Directional control of a platoon of vehicles for comfort specification by considering parasitic time delays and lags. PROMET–Traffic & Transportation. 2013;25(5):412-420.
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.
Swaroop D, Hedrick JK. Constant spacing strategies for platooning in automated highway systems. ASME Journal of Dynamic System Measurement and Control. 1999;121(3):462-470.
Seiler P, Pant A, Hedrick JK. Disturbance propagation in vehicle strings. IEEE Transactions on Automatic Control. 2004;49(10):1835-1841.
Khatir ME, Davision EJ. Decentralized control of a large platoon of vehicles using non-identical controllers. in Proceedings of the 2004 American Control Conference; 2004 Jun 30-Jul 2; Boston, USA; 2004.
Tanner HG, Christodoulakis DK. Decentralized cooperative control of heterogeneous vehicle groups. Robotics and autonomous systems. 2007;55(11):811-823.
Hogan N. Impedance control: An approach to manipulation: Part I-Theory. ASME Journal of Dynamic System Measurement and Control. 1985;107(1):1-7.
Horn BKP. Suppressing traffic flow instabilities. Proceedings of the 16th International IEEE Annual Conference on Intelligent Transportation Systems; 2013 Oct 6-9; Hague, Netherlands; 2013.
Liu X, Goldsmith A, Mahal SS, Hedrick JK. Effects of communication delay on string stability in vehicle platoons. IEEE Proceedings of the Intelligent Transportation Systems; 2001 Aug 25-29; Oakland, USA; 2001.
Ling-Yun X, Feng G. Effect of information delay on string stability of platoon of automated vehicles under typical information frameworks. Journal of Central South University of Technology. 2010;17(6):1271-1278.
Sinan O, Wouw VD, Heemels N, Maurice HWP, Henk N. String stability of interconnected vehicles under communication constraints. in Proceeding of the IEEE Conference Decision and Control; 2012 Dec 10-13; Maui, USA; 2012.
Yi SY, Chong KT. Impedance control for a vehicle platoon system. Mechatronics. 2005;15(5):627-638.
Hao H, Barooah P, Mehta PG. Stability margin scaling laws for distributed formation control as a function of network structure. IEEE Transactions on Automatic Control. 2011;56(4):923-929.
Fernandes P, Nunes U. Platooning with IVC-enabled autonomous vehicles: strategies to mitigate communication delays, improve safety and traffic Flow. IEEE Transactions on Intelligent Transportation Systems. 2012;13(1):91-106.
Fazelinia H, Sipahi R, Olgac N. Stability robustness analysis of multiple time-delayed systems using building block concept. IEEE Transactions on Automatic Control. 2007;52(5)799-810.
Cepeda-Gomez R, Olgac N. An exact methodology for the stability analysis of linear consensus protocols with time delay. IEEE Transactions on Automatic Control. 2011;56(7):1734-1740.
Stankovic SS, Stanojevic M, Siljak, DD. Decentralized suboptimal LQ control of a platoon. Transportation System; 1997 Jun 16-18; Chania, Greece; 1997.
Sheikholeslam Sh, Desoer ChA. Longitudinal control of a platoon of vehicles, IEEE American Control Conference; 1990 May 23-25; San Diego, USA; 1990.
Schaefer RD. An Introduction to nonassociative algebras. New York: Dover; 1996.
Cao Y, Ren W. Containment control with multiple stationary or dynamic leaders under a directed interaction graph. in Proceeding of the IEEE Conference Decision Control; 2009 Dec 15-18; Shanghai, China; 2009.
Cepeda-Gomez R. Exact and exhaustive stability analysis of linear consensus protocols with time-delay, PhD. Dissertation, University of Connecticut, Storrs, CT, 2012.
Da Fonseca C.M, Veerman J.J.P. On the spectra of certain directed paths. Applied Mathematics Letters. 2009;22(9):1351-1355.
Olgac N, Sipahi R. Complete stability robustness of third-order LTI multiple time-delay systems. Automatica. 2005;41(8):1413-1422.
Ergenc AF, Olgac N, Fazelinia H. Extended kronecker summation for cluster treatment of LTI systems with multiple delays. SIAM Journal on Control and Optimization. 2007;46(1):143-155.
Fazelinia H. A novel stability analysis of systems with multiple time delays and its application to high speed milling chatter. PhD. Dissertation, University of Connecticut, Storrs, CT;2007.
Nia PM, Sipahi R. Controller design for delay-independent stability of linear time-invariant vibration systems with multiple delays. Journal of Sound and Vibration. 2013;332(14):3589-3604.
Michiels W, Niculescu SI. Stability and stabilization of time delay systems: An eigenvalue-based approach. SIAM, Advances in Design and Control; Philadelphia, USA; 2007.
Ekasius Z. V. A Stability test for systems with delays. Proceeding Joint Automatic Control Conference, 1980; San Francesco, USA; 1980.
Sipahi R, Olgac N. An unique methodology for the stability robustness of multiple time delay systems. Systems & Control Letters. 2006;55(10):819-825.
Yanakiev D, Kanellakopoulos I. A simplified framework for string stability analysis in AHS. in Proceeding of the 13th IFAC World Congress, 1996 Jul; San Francisco, USA; 1996.
Cook P. Conditions for string stability. System and Control Letters. 2005;54(10):991-998.
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