This paper addresses the problem of platoon control. The stability and the string stability of a platoon of vehicles in the simultaneous presence of the time delay and the lag are investigated. The contribution of this paper is twofold. First, the paradigm of the cluster treatment of characteristic roots is utilized in order to reveal the stabilizing parametric regions in the domain of the delays to render the stability of a closed-loop system. Second, the restrictions which need to be imposed on the control parameters are considered in order to make the vehicle behave monotonically in the forward direction without collision as well as the requirement for the string stability. Finally, an example of multiple-vehicle platoon control is presented, which demonstrates the effectiveness and the robustness of the proposed method.
GhasemiAKazemiRAzadiS. Stable decentralized control of platoon of vehicles with heterogeneous information feedback. IEEE Trans Veh Technol2013; 62(7): 4299–4308.
2.
HaoHBarooahP. Control of large 1D networks of double integrator agents: role of heterogeneity and asymmetry on stability margin. In: 2010 49th IEEE conference on decision and control, Atlanta, Georgia, USA, 15–17 December 2010, pp. 7395–7400. New York: IEEE.
3.
TangermanFMVeermanJJPStosicBD. Asymmetric decentralized flocks. IEEE Trans Autom Control2012; 57: 2844–2853.
4.
GuoGYueW. Hierarchical platoon control with heterogeneous information feedback. IET Control Theory Applic2011; 5(15): 1766–1781.
5.
DunbarWBCaveneyDS. Distributed receding horizon control of vehicle platoons: stability and string stability. IEEE Trans Autom Control2012; 57(3): 620–633.
6.
XiaoLGaoF. Practical string stability of platoon of adaptive cruise control vehicles. IEEE Trans Intell Transpn Systems2011; 12(4): 1184–1194.
7.
MiddletonRBraslavskyJ. String instability in classes of linear time invariant formation control with limited communication range. IEEE Trans Autom Control2010; 55(7): 1519–1530.
8.
ZhouJPengH. Range policy of adaptive cruise control vehicle for improved flow stability and string stability. IEEE Trans Intell Transpn Systems2005; 6(2): 229–237.
9.
SwaroopDHedrickJK. Constant spacing strategies for platooning in automated highway systems. Trans ASME, J Dynamic Systems, Measmt, Control1999; 121: 462–470.
10.
SeilerPPantAHedrickJK. Disturbance propagation in vehicle strings. IEEE Trans Autom Control2004; 49(10): 1835–1841.
11.
GhasemiAKazemiRAzadiS. Directional control of a platoon of vehicles for comfort specification by considering parasitic time delays and lags. PROMET – Traffic Transpn2013; 25(5): 412–420.
12.
FernandesPNunesU. Platooning with IVC-enabled autonomous vehicles: strategies to mitigate communication delays, improve safety and traffic flow. IEEE Trans Intell Transpn Systems2012; 13(1): 91–106.
13.
YueWGuoG. Guaranteed cost adaptive control of nonlinear platoons with actuator delay. Trans ASME, J Dynamic Systems, Measmt, Control2012; 134: 051012 (11 pp.).
14.
GhasemiAKazemiRAzadiS. Stability analysis of longitudinal control of a platoon of vehicles by considering lags subject to communication delay. Int J Innovative Comput, Inf Control2014; 10(5): 1625–1641.
15.
GuoGYueW. Autonomous platoon control allowing range-limited sensors., IEEE Trans Veh Technol, 2012; 61(7): 2901–2912.
16.
BamiehBJovanovićMRMitraPPattersonS. Coherence in large-scale networks: dimension dependent limitations of local feedback. IEEE Trans Autom Control2012; 57(9): 2235–2249.
17.
LinFFardadMJovanovićMR. Optimal control of vehicular formations with nearest neighbor interactions. IEEE Trans Autom Control2012; 57(9): 2203–2218.
18.
FazeliniaHSipahiROlgacN. Stability robustness analysis of multiple time-delayed systems using building block concept. IEEE Trans Autom Control2007; 52: 799–810.
19.
Cepeda-GomezROlgacN. An exact methodology for the stability analysis of linear consensus protocols with time delay. IEEE Trans Autom Control2011; 56: 1734–1740.
20.
MartinezJ-JCanudas-de-WitC. A safe longitudinal control for adaptive cruise control and stop-and-go scenarios. IEEE Trans Control Systems Technol2007; 5(2): 246–258.
21.
CookP. Stable control of vehicle convoys for safety and comfort. IEEE Trans Autom Control2007; 52(3): 526–531.
22.
LeuYGWangWYLeeTT. Robust adaptive fuzzy-neural controllers for uncertain nonlinear systems. IEEE Trans Robotics Automn1999; 15(5): 805–817.
23.
StankovicSSStanojevicMSiljakDD. Decentralized suboptimal LQ control of a platoon. In: 8th IFAC/IFIP/IFORS symposium on transportation systems, Chania, Greece, 16–18 June 1997, Vol 1, pp. 81–86. Oxford: Elsevier.
24.
SheikholeslamSDesoerCA. Longitudinal control of a platoon of vehicles. In: IEEE American control conference, San Diego, California, USA, 23–25 May 1990, pp. 291–296. New York: IEEE.
25.
NiaPMSipahiR. Controller design for delay-independent stability of linear time-invariant vibration systems with multiple delays. J Sound Vibr2013; 332(14): 3589–3604.
26.
MichielsWNiculescuS-I. Stability and stabilization of time-delay systems: an eigenvalue-based approach, Advances in Design and Control, Vol 12. Philadelphia, Pennsylvania: SIAM, 2007.
27.
Cepeda-GomezR. Exact and exhaustive stability analysis of linear consensus protocols with time-delay. PhD Thesis, University of Connecticut, Storrs, Connecticut, USA, 2012.
28.
YanaKievDKanellakopoulosI. A simplified framework for string stability analysis in AHS. In: 13th IFAC world congress, San Francisco, California, USA, 30 June–5 July 1996, pp. 177–182. Oxford: Pergamon.
29.
CookP. Conditions for string stability. System Control Lett2005; 54: 991–998.
30.
KurtzDC. A sufficient condition for all the roots of a polynomial to be real. Am Mathl Mon1992; 99(3): 259–263.
31.
NieuwenhuijzeMRI. String stability analysis of bidirectional adaptive cruise control. Master’s Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2010.
32.
NausGVugtsRPloegJ. String-stable CACC design and experimental validation: A frequency-domain approach. IEEE Trans Veh Technol2010; 59: 4268–4279.
33.
GhasemiAKazemiRAzadiS. Stabilty analysis of bidirectional adaptive cruise control with asymmetric information flow. Proc IMechE Part C: J Mechanical Enginering Science; 229(2): 216–226.
