<p>This paper delves into the robust optimal longitudinal control of connected and automated vehicle (CAV) platoons under parameter uncertainties and external disturbances. String stability not only can contribute to disturbance attenuation throughout a vehicle platoon, but also helps to enhance traffic capacity. However, the existing achievements lack explicit consideration for string stability in the robust optimal longitudinal control of CAV platoons. To this end, a robustly string stable optimal control method is developed with explicit consideration of parameter uncertainties, exogenous disturbances, and string stability. First of all, the inverse dynamics control approach is exploited to exactly linearize the nonlinear longitudinal dynamics. Then, we formulate a multi-objective optimization problem considering physical limitations, ride safety, passenger comfort, and control efficiency. To facilitate the control design process, the parameter uncertainties and the exogenous disturbances are lumped into a single disturbance. After that, a finite time disturbance observer (FTDO) is employed to separately estimate the lumped disturbance and the preceding vehicle acceleration, reducing communication burden. Based on the estimation, we develop a FTDO-based tube model predictive control (TMPC) algorithm. Moreover, we prove the recursive feasibility of the proposed algorithm and rigorously analyze individual stability of each vehicle and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_10964_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathcal {L}}_\infty $</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">L</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> string stability of whole CAV platoon. Extensive simulations demonstrate the effectiveness of our method in both homogeneous and heterogeneous platoons, showing significant improvements in spacing error reduction compared with traditional TMPC. This work advances the field by providing a comprehensive solution that combines disturbance rejection, predictive control, and explicit string stability constraints, offering a promising approach for safe and efficient CAV platoon control in real-world scenarios.</p>

String stable and robust optimal longitudinal control for vehicle platoons: a finite time disturbance observer-based tube MPC

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发表日期：

2025年2月17日

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Qian Chen,
Daniel Jian Sun,
Jingxin Xia,
Xiufeng Liu,
Chengchuan An

摘要

This paper delves into the robust optimal longitudinal control of connected and automated vehicle (CAV) platoons under parameter uncertainties and external disturbances. String stability not only can contribute to disturbance attenuation throughout a vehicle platoon, but also helps to enhance traffic capacity. However, the existing achievements lack explicit consideration for string stability in the robust optimal longitudinal control of CAV platoons. To this end, a robustly string stable optimal control method is developed with explicit consideration of parameter uncertainties, exogenous disturbances, and string stability. First of all, the inverse dynamics control approach is exploited to exactly linearize the nonlinear longitudinal dynamics. Then, we formulate a multi-objective optimization problem considering physical limitations, ride safety, passenger comfort, and control efficiency. To facilitate the control design process, the parameter uncertainties and the exogenous disturbances are lumped into a single disturbance. After that, a finite time disturbance observer (FTDO) is employed to separately estimate the lumped disturbance and the preceding vehicle acceleration, reducing communication burden. Based on the estimation, we develop a FTDO-based tube model predictive control (TMPC) algorithm. Moreover, we prove the recursive feasibility of the proposed algorithm and rigorously analyze individual stability of each vehicle and ${\mathcal {L}}_\infty $ $L_{\infty}$ string stability of whole CAV platoon. Extensive simulations demonstrate the effectiveness of our method in both homogeneous and heterogeneous platoons, showing significant improvements in spacing error reduction compared with traditional TMPC. This work advances the field by providing a comprehensive solution that combines disturbance rejection, predictive control, and explicit string stability constraints, offering a promising approach for safe and efficient CAV platoon control in real-world scenarios.