Stability analysis of the vehicle platoon system considering predecessor following and time-varying delay

doi:10.3969/j.issn.1674-8484.2023.04.008

Abstract

Abstract:

In order to improve the safety of vehicle queuing, a delay-dependent stability analysis method based on Lyapunov-Krasovskii functional (LKF) was proposed to estimate the range of allowable time delay for vehicle following system with time-varying delay. For the vehicle following system with time-varying delay, a system model with double time-varying delay was established. Considering the relationship between two time-varying delay variables, LKF was constructed, and the stability criterion of the system with double time-varying delay was given after processing by matrix inequalities. The allowable range of time delay under different control parameters was calculated by MATLAB software for 4 vehicle lines. The results show that the controller gain is inversely proportional to the maximum time delay allowed by the system under the parameters of the vehicle following system; and under the same parameters, the delay is more important to the high-speed vehicle queue; The proposed stability analysis method can obtain the maximum allowable time delay to ensure the stability of the system, and provide stability criteria for designing the controller of the actual vehicle following queue.

Key words: vehicle platoon system, time-varying delay, stability analysis, Lyapunov-Krasovskii functional(LKF)

CLC Number:

U461.6

ZHOU Liguang, XU Hang, SHANGGUAN Xingchen, YAN Chen. Stability analysis of the vehicle platoon system considering predecessor following and time-varying delay[J]. Journal of Automotive Safety and Energy, 2023, 14(4): 463-471.

Figures/Tables 6

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误差补偿矩阵U	时滞变量上界τ₂(t)
误差补偿矩阵U	K_p = 0.7	K_p = 0.9	K_p = 1.0	K_p = 1.1
[0.4 1.0 0]	0.730 7	0.577 9	0.517 8	0.465 1
[0.5 1.0 0]	0.575 0	0.463 6	0.421 1	0.379 2
[0.9 1.0 0]	0.172 6	0.137 0	0.118 4	0.101 8
[1.0 1.0 0]	0.103 8	0.075 9	0.063 7	0.048 6

误差补偿矩阵U	时滞变量上界τ₂(t)
误差补偿矩阵U	K_p = 0.7	K_p = 0.9	K_p = 1.0	K_p = 1.1
[0.4 1.0 0]	0.730 7	0.577 9	0.517 8	0.465 1
[0.5 1.0 0]	0.575 0	0.463 6	0.421 1	0.379 2
[0.9 1.0 0]	0.172 6	0.137 0	0.118 4	0.101 8
[1.0 1.0 0]	0.103 8	0.075 9	0.063 7	0.048 6