On the peaking phenomenon in the control of vehicular platoons

We investigate the peaking phenomenon in the control of large-scale vehicular platoons. These systems are of considerable practical importance as they represent an example of systems on lattices in which different subsystems are dynamically coupled only through feedback controls. We demonstrate that imposing a uniform rate of convergence for all vehicles towards their desired trajectories may generate large transient peaks in both velocity and control. We further derive explicit constraints on feedback gains ‐ for any given set of initial conditions ‐ to achieve desired position transients without magnitude and rate peaking. These constraints are used to generate the trajectories around which the states of the platoon system are driven towards their desired values without the excessive use of control effort. All results are illustrated using computer simulations of platoons containing a large number of vehicles. c 2007 Elsevier B.V. All rights reserved.

[1]  Randal W. Beard,et al.  A coordination architecture for spacecraft formation control , 2001, IEEE Trans. Control. Syst. Technol..

[2]  S. Lall,et al.  Decentralized control information structures preserved under feedback , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[3]  J.K. Hedrick,et al.  Longitudinal Vehicle Controller Design for IVHS Systems , 1991, 1991 American Control Conference.

[4]  J.M. Fowler,et al.  A formation flight experiment , 2003, IEEE Control Systems.

[5]  Pravin Varaiya,et al.  Smart cars on smart roads: problems of control , 1991, IEEE Trans. Autom. Control..

[6]  Dimitry M. Gorinevsky,et al.  Structured uncertainty analysis of robust stability for multidimensional array systems , 2003, IEEE Trans. Autom. Control..

[7]  J. K. Hedrick,et al.  Constant Spacing Strategies for Platooning in Automated Highway Systems , 1999 .

[8]  Petar V. Kokotovic,et al.  Path-following for a class of nonlinear systems with unstable zero dynamics , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[9]  U. Grenander,et al.  Toeplitz Forms And Their Applications , 1958 .

[10]  A. Teel.  Global stabilization and restricted tracking for multiple integrators with bounded controls , 1992 .

[11]  R. E. Kalman,et al.  When Is a Linear Control System Optimal , 1964 .

[12]  João Pedro Hespanha,et al.  Path-following for nonminimum phase systems removes performance limitations , 2005, IEEE Transactions on Automatic Control.

[13]  S. Melzer,et al.  Optimal regulation of systems described by a countably infinite number of objects , 1971 .

[14]  Fernando Paganini,et al.  Convex synthesis of localized controllers for spatially invariant systems , 2002, Autom..

[15]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[16]  Fernando Paganini,et al.  A method for decentralized control design in spatially invariant arrays , 2003, Proceedings of the 2003 American Control Conference, 2003..

[17]  Nick McKeown,et al.  Automated vehicle control developments in the PATH program , 1991 .

[18]  J.K. Hedrick,et al.  Direct adaptive longitudinal control of vehicle platoons , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[19]  Geir E. Dullerud,et al.  Distributed control of heterogeneous systems , 2004, IEEE Transactions on Automatic Control.

[20]  Fernando Paganini,et al.  Distributed control of spatially invariant systems , 2002, IEEE Trans. Autom. Control..

[21]  Andrew G. Sparks,et al.  Spacecraft formation flying: dynamics and control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[22]  R. D'Andrea,et al.  Distributed control of close formation flight , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[23]  Joao P. Hespanha,et al.  Path-following or reference tracking? , 2004 .

[24]  K. Chu.  Decentralized Control of High-Speed Vehicular Strings , 1974 .

[25]  Petros A. Ioannou,et al.  Vehicle following control design for automated highway systems , 1997, 1997 IEEE 47th Vehicular Technology Conference. Technology in Motion.

[26]  D. F. Chichka,et al.  Solar-powered, formation-enhanced aerial vehicle systems for sustained endurance , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[27]  J. Hedrick,et al.  String stability of interconnected systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[28]  Andrew R. Teel,et al.  Control of linear systems with saturating actuators , 1996 .

[29]  Frank L. Lewis,et al.  Optimal Control , 1986 .

[30]  Petros G. Voulgaris,et al.  Optimal H2 controllers for spatially invariant systems with delayed communication requirements , 2003, Syst. Control. Lett..

[31]  Andrew G. Sparks,et al.  Adaptive output feedback tracking control of spacecraft formation , 2002 .

[32]  Peter Seiler,et al.  Disturbance propagation in vehicle strings , 2004, IEEE Transactions on Automatic Control.

[33]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[34]  Mihailo R. Jovanovic,et al.  On the ill-posedness of certain vehicular platoon control problems , 2005, IEEE Transactions on Automatic Control.

[35]  Mihailo R. Jovanovic,et al.  Lyapunov-based distributed control of systems on lattices , 2005, IEEE Transactions on Automatic Control.

[36]  M. Athans,et al.  On the optimal error regulation of a string of moving vehicles , 1966 .

[37]  Geir E. Dullerud,et al.  Distributed control design for spatially interconnected systems , 2003, IEEE Trans. Autom. Control..

[38]  T. Keviczky,et al.  Distributed LQR Design for Dynamically Decoupled Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[39]  Cédric Langbort,et al.  Distributed control design for systems interconnected over an arbitrary graph , 2004, IEEE Transactions on Automatic Control.