Safe Stabilizing Control of Traffic Systems With Simultaneous State and Actuator Delays

Zhao, Chenguang; Yu, Huan · 2024 · IEEE Control Systems Letters

DOI: 10.1109/lcsys.2024.3411828

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Summary

This paper addresses the challenge of ensuring formal safety guarantees for traffic systems involving Connected and Automated Vehicles (CAVs) when subjected to simultaneous state and actuator delays. While previous research has focused on delay-free systems or systems with only one type of delay, real-world traffic involves intrinsic delays from human reaction times (state delays) and sensor/actuator latencies (actuator delays). These delays can cause safety violations in controllers designed for delay-free systems. The authors aim to solve the safe stabilization problem for a string of vehicles by designing a control barrier function (CBF) framework that accounts for both delay types and external disturbances from the leading vehicle. The methodology involves modeling the longitudinal dynamics of a vehicle chain consisting of a head vehicle, a CAV, and $N$ follower vehicles. The system is linearized around equilibrium states to derive a state-space representation with time delays. To compensate for actuator delay, the authors design a state predictor with bounded prediction error, accounting for the unknown future speed of the head vehicle. They derive robust safety constraints by embedding distributed state delays into the predictor state. A safety-critical controller is synthesized by solving a Quadratic Programming (QP) problem that minimizes deviation from a nominal stabilizing controller while satisfying the derived CBF constraints. The CAV’s safety is prioritized over follower vehicles’ safety by introducing slack variables into the latter’s constraints to ensure QP feasibility. Numerical simulations validate the proposed approach in two safety-critical scenarios: sudden deceleration of the head vehicle and accidental acceleration of a follower vehicle. The results demonstrate that the proposed safety-critical controller maintains formal safety guarantees under simultaneous delays. In contrast, a nominal controller and a CBF designed only for actuator delays (ignoring state delays) fail to prevent safety violations, such as rear-end collisions, when state delays are present. Specifically, when a follower vehicle accelerates unexpectedly, the proposed controller correctly adjusts the CAV’s speed to maintain safe spacing, whereas the delay-ignoring CBF fails to do so. The significance of this work lies in providing the first theoretical result for safety-critical control of linearized traffic systems with both actuator and state delays. It highlights the critical impact of state delays on safety, showing that ignoring them can lead to unsafe outcomes even if actuator delays are compensated. The proposed framework offers a robust solution for integrating CAVs into mixed traffic environments, ensuring stability and safety despite the inherent delays and disturbances present in real-world driving conditions.

Key finding

The proposed control barrier function design with delay compensation successfully guarantees formal safety for traffic systems with simultaneous state and actuator delays, whereas controllers ignoring state delays fail to prevent safety violations.

Methodology

simulation_modeling

Provenance

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Topics

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• teleoperation remote driving