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Backstepping method based controller design for third-order truck platoon robust to dynamic uncertainty and external disturbance

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Abstract

The vehicle platoon is subject to dynamic uncertainty and external disturbance, such as air drag and parameter variation in practice, so lack of consideration for those factors can deteriorate control performance. This paper proposes a nonlinear control algorithm based on a novel adaptive backstepping method to cope with the uncertainty and disturbance. The virtual controller in the backstepping method utilizes only the local information of the individual vehicle, rather than the global state information, in the control algorithm design. A third-order vehicle dynamics model was built to incorporate the nonlinearity and the factor of actuation delay. The fuzzy logic system (FLS) is applied to estimate the nonlinearity in vehicle dynamics to facilitate the adaptive control. Five scenarios with different settings were constructed to verify the control performance in the simulation, which indicates the effectiveness and robustness of the controller to dynamic uncertainty and external disturbance.

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Abbreviations

\({{\cal G}_n}\) :

Directed graph of the communication network

\({{\cal V}_n}\) :

Vertices in the graph

\({{\cal E}_n}\) :

The set of edges in the graph

\({{\cal A}_n}\) :

The adjacency matrix associated with \({{\cal G}_n}\)

\({\cal V}_n^s\) :

The vertices in the directed subgraph

\({\cal E}_n^s\) :

The set of edges in the subgraph

\({{\cal N}_i}\) :

Neighbors of node i in \({{\cal G}_n}\)

L :

The Laplacian matrix of the graph \({{\cal G}_n}\)

ϕ(x):

The fuzzy function vector

\({\mu _{F_i^l}}\left( {{x_i}} \right)\) :

The membership function of the linguistic variable

θ*:

The optimal fuzzy parameter vector

f j(x j):

Nonlinear Term in vehicle dynamics model

d j :

The external disturbance

u j :

The control input

m j :

Mass of vehicle node j

C Ad :

Air drag coefficient

z :

Changed coordinate vector

α 2j ,α 3j :

Virtual controllers

ε j :

Minimal approximation error in FLS

\({\tilde \theta _j}\) :

The estimation error of the fuzzy parameter

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Acknowledgments

This work was supported by National Natural Science Foundation of China (51875032), (52002025), Natural Science Foundation of Beijing Municipality (8202015), and Subsidy for Young Teachers’ Scientific Research Ability Improvement Program (X21050).

Author information

Authors and Affiliations

  1. Beijing University of Civil Engineering and Architecture, Beijing, 100044, China

    Jianbo Feng, Liyang He, Yanxue Wang & Jianwei Yang

  2. Beijing Institute of Technology, Beijing, 100081, China

    Hongbin Ren

Authors
  1. Jianbo Feng
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  2. Liyang He
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  3. Yanxue Wang
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  4. Jianwei Yang
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  5. Hongbin Ren
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Contributions

Dr. Feng conducted the major research work, Miss He was responsible for the major revision work, Dr. Wang established the simulation platform, Dr. Yang assisted in the whole process, and Dr. Ren provided technical support.

Corresponding author

Correspondence to Jianbo Feng.

Additional information

Jianbo Feng received the Ph.D. in Vehicle Engineering at the Beijing Institute of Technology. From October 2016 to October 2018, he studied at the Vehicle Dynamics Laboratory, University of California at Berkeley. He is now a Lecturer at Beijing University of Civil Engineering and Architecture, Beijing. His research interests include vehicle platoon control, vehicle dynamics and control, intelligent driver assistance system.

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Feng, J., He, L., Wang, Y. et al. Backstepping method based controller design for third-order truck platoon robust to dynamic uncertainty and external disturbance. J Mech Sci Technol 37, 1433–1442 (2023). https://doi.org/10.1007/s12206-023-0229-8

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  • DOI: https://doi.org/10.1007/s12206-023-0229-8

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