[Paper Review] Cooperative Extended State Observer Based Control of Vehicle Platoons With Arbitrarily Small Time Headway

Anquan Liu, Tao Li+2 more|arXiv (Cornell University)|Apr 21, 2020

Traffic control and management17 references4 citations

TL;DR

This paper proposes a cooperative extended state observer-based control law for vehicle platoons under the constant time headway policy, enabling both closed-loop and $\mathcal{L}_{2}$ string stability with arbitrarily small time headways. The method uses only on-board sensor measurements (distance, velocity, acceleration, and relative velocity) to estimate inter-vehicle acceleration differences via distributed observers, eliminating reliance on wireless communication and ensuring robustness to delays, noise, and uncertainties.

ABSTRACT

We study platoon control of vehicles with linear third-order longitudinal dynamics under the constant time headway policy. The controller of each follower vehicle is only based on its own velocity, acceleration, inter-vehicle distance and velocity difference with respect to its immediate predecessor, which are all obtained by on-board sensors. We develop distributed cooperative extended state observers for followers to estimate the acceleration differences between adjacent vehicles. Based on estimates of the acceleration differences, distributed cooperative control laws are designed. By using the stability theory of perturbed linear systems, we show that the control parameters can be properly designed to ensure the closed-loop and L2 string stabilities for any given positive time headway. We further show that the proposed control law based on the ideal vehicle model can guarantee the closed-loop and L2 string stabilities even if there are small model parameter uncertainties. Also, simulation results demonstrate the robustness of the proposed control law against sensing noises, input delays and parameter uncertainties.

Motivation & Objective

• To design a distributed control law for vehicle platoons that ensures stability under arbitrarily small time headways without relying on inter-vehicle communication.
• To address the practical limitation of unreliable or absent wireless communication in vehicle platooning by using only on-board sensor data.
• To guarantee both closed-loop and $\mathcal{L}_{2}$ string stability for linear third-order vehicle dynamics under the constant time headway policy.
• To provide explicit, quantitative ranges for control parameters that ensure stability across all positive time headway values.
• To demonstrate robustness against sensing noise, input delays, and model parameter uncertainties through theoretical analysis and simulations.

Proposed method

• Develops distributed cooperative extended state observers to estimate acceleration differences between adjacent vehicles using only local on-board measurements.
• Designs a distributed control law per follower vehicle composed of a feedback term (based on inter-vehicle distance error and its derivative) and a feedforward term (based on estimated preceding vehicle acceleration).
• Decomposes the closed-loop system matrix into a nominal part and a perturbation part to apply stability theory of perturbed linear systems.
• Uses frequency-domain analysis of transfer functions to derive conditions for $\mathcal{L}_{2}$ string stability.
• Establishes explicit, quantitative bounds on control parameters (e.g., $\mu_p$, $\mu_v$, $\mu_a$) in terms of system parameters to ensure stability for any positive time headway.
• Validates robustness through theoretical analysis and numerical simulations under sensing noise, input delays, and parameter uncertainties.

Experimental results

Research questions

• RQ1 Can a distributed control law be designed that ensures both closed-loop and $\mathcal{L}_{2}$ string stability for vehicle platoons with arbitrarily small time headways using only on-board sensor data?
• RQ2 How can inter-vehicle acceleration differences be accurately estimated in the absence of wireless communication?
• RQ3 What explicit, quantitative ranges of control parameters guarantee stability for any positive time headway in a linear third-order vehicle model?
• RQ4 How does the proposed method maintain stability under sensing noise, input delays, and model uncertainties compared to prior communication-dependent approaches?
• RQ5 Can the stability analysis be rigorously proven using perturbed linear system theory and frequency-domain transfer function analysis?

Key findings

• The proposed control law ensures both closed-loop and $\mathcal{L}_{2}$ string stability for any given positive time headway, including arbitrarily small values.
• Explicit, quantitative ranges for control parameters ($\mu_p$, $\mu_v$, $\mu_a$) are derived in terms of system parameters to guarantee stability.
• The method achieves stability without relying on wireless communication, using only on-board sensors to estimate acceleration differences via cooperative extended state observers.
• Theoretical analysis confirms that the system remains stable under sensing noise, input delays, and small model parameter uncertainties.
• Simulation results demonstrate robust performance under various realistic disturbances, validating the theoretical claims.
• The transfer function analysis proves $\|G_{ei}(s)\|_{\infty} \leq 1$, confirming $\mathcal{L}_{2}$ string stability across all frequencies.