On L∞ string stability of nonlinear bidirectional asymmetric heterogeneous platoon systems

This paper is concerned with the study of bidirectionally coupled platoon systems. The case considered is when the vehicles are heterogeneous and the coupling can be nonlinear and asymmetric. For such systems, a sufficient condition for L∞ string stability is presented. The effectiveness of our approach is illustrated via a numerical example, where it is shown how our result can be recast as an optimization problem, allowing to design the control protocol for each vehicle independently on the other vehicles and hence leading to a bottom-up approach for the design of string stable systems able to track a time-varying reference speed.

[1]  Mario di Bernardo,et al.  Global Entrainment of Transcriptional Systems to Periodic Inputs , 2009, PLoS Comput. Biol..

[2]  Nathan van de Wouw,et al.  Lp String Stability of Cascaded Systems: Application to Vehicle Platooning , 2014, IEEE Transactions on Control Systems Technology.

[3]  C. Canudas de Wit,et al.  Stability issues for vehicle platooning in automated highway systems , 1999, Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328).

[4]  C. Desoer,et al.  The measure of a matrix as a tool to analyze computer algorithms for circuit analysis , 1972 .

[5]  Nathan van de Wouw,et al.  Controller Synthesis for String Stability of Vehicle Platoons , 2014, IEEE Transactions on Intelligent Transportation Systems.

[6]  Ivo Herman,et al.  Disturbance scaling in bidirectional vehicle platoons with different asymmetry in position and velocity coupling , 2017, Autom..

[7]  Ioannis Kanellakopoulos,et al.  Nonlinear spacing policies for automated heavy-duty vehicles , 1998 .

[8]  Karl Henrik Johansson,et al.  String Stability and a Delay-Based Spacing Policy for Vehicle Platoons Subject to Disturbances , 2017, IEEE Transactions on Automatic Control.

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

[10]  Eduardo Sontag.  Input to State Stability: Basic Concepts and Results , 2008 .

[11]  Dan Martinec,et al.  Scaling in Bidirectional Platoons With Dynamic Controllers and Proportional Asymmetry , 2014, IEEE Transactions on Automatic Control.

[12]  M. Vidyasagar,et al.  Nonlinear systems analysis (2nd ed.) , 1993 .

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

[14]  L. Peppard.  String stability of relative-motion PID vehicle control systems , 1974 .

[15]  Prashant G. Mehta,et al.  Stability Margin Scaling Laws for Distributed Formation Control as a Function of Network Structure , 2010, IEEE Transactions on Automatic Control.

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

[17]  Dan Martinec,et al.  On the Necessity of Symmetric Positional Coupling for String Stability , 2016, IEEE Transactions on Control of Network Systems.

[18]  Swaroop Darbha,et al.  Effects of V2V communication on time headway for autonomous vehicles , 2017, 2017 American Control Conference (ACC).

[19]  Nakayama,et al.  Dynamical model of traffic congestion and numerical simulation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  J. Hedrick,et al.  String stability of interconnected systems , 1996, IEEE Trans. Autom. Control..

[21]  Giovanni Russo,et al.  On the Design of Nonlinear Distributed Control Protocols for Platooning Systems , 2017, IEEE Control Systems Letters.

[22]  Jeroen Ploeg,et al.  Consensus Control for Vehicular Platooning With Velocity Constraints , 2018, IEEE Transactions on Control Systems Technology.

[23]  Dirk Aeyels,et al.  Vehicle Platoons Through Ring Coupling , 2008, IEEE Transactions on Automatic Control.

[24]  Domitilla Del Vecchio,et al.  A contraction approach to input tracking via high gain feedback , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[25]  Mario di Bernardo,et al.  Distributed Consensus Strategy for Platooning of Vehicles in the Presence of Time-Varying Heterogeneous Communication Delays , 2015, IEEE Transactions on Intelligent Transportation Systems.

[26]  Le Yi Wang,et al.  Stability Margin Improvement of Vehicular Platoon Considering Undirected Topology and Asymmetric Control , 2016, IEEE Transactions on Control Systems Technology.

[27]  Richard H. Middleton,et al.  Vehicular Platoons in cyclic interconnections with constant inter-vehicle spacing , 2017 .

[28]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[29]  Mario di Bernardo,et al.  A Contraction Approach to the Hierarchical Analysis and Design of Networked Systems , 2013, IEEE Transactions on Automatic Control.

[30]  João Pedro Hespanha,et al.  Mistuning-Based Control Design to Improve Closed-Loop Stability Margin of Vehicular Platoons , 2008, IEEE Transactions on Automatic Control.

[31]  Douglas J. Leith,et al.  $\mathcal{L}_2$ and $\mathcal{L}_{\infty}$ Stability Analysis of Heterogeneous Traffic With Application to Parameter Optimization for the Control of Automated Vehicles , 2016, IEEE Transactions on Control Systems Technology.

[32]  Karl H. Johansson,et al.  Heavy-Duty Vehicle Platooning for Sustainable Freight Transportation: A Cooperative Method to Enhance Safety and Efficiency , 2015, IEEE Control Systems.

[33]  D. Swaroop,et al.  A review of constant time headway policy for automatic vehicle following , 2001, ITSC 2001. 2001 IEEE Intelligent Transportation Systems. Proceedings (Cat. No.01TH8585).

[34]  Richard H. Middleton,et al.  Scalability of bidirectional vehicle strings with static and dynamic measurement errors , 2015, Autom..

[35]  Richard H. Middleton,et al.  Passivity-based control for multi-vehicle systems subject to string constraints , 2014, Autom..

[36]  Richard H. Middleton,et al.  String Instability in Classes of Linear Time Invariant Formation Control With Limited Communication Range , 2010, IEEE Transactions on Automatic Control.

[37]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[38]  Zhen Kan,et al.  On the robustness of large 1-D network of double integrator agents , 2012, 2012 American Control Conference (ACC).