Multi-Objective $H_{\infty}$ Control for String Stability of Cooperative Adaptive Cruise Control Systems (2103.13830v1)

Abstract: Autonomous vehicle following systems are playing a decisive role to increase vehicle density on roads by shortening inter-vehicle time gaps. However, disturbance attenuation along a platoon of vehicles, i.e., string stability, is being a challenging task while time gap is getting shorter. In order to guarantee the string stability of a vehicle platoon, a multi-objective $H_{\infty}$ control formulation for adaptive cruise control and cooperative adaptive cruise control structures has been investigated in this paper. The proposed control method solves an optimization problem and achieves a controller that is able to provide not only the system stability, but also the string stability as distinct from the traditional $H_{\infty}$ control.

• The paper presents a multi-objective H∞ control strategy that integrates string stability into ACC and CACC systems.
• It employs a decentralized control design with techniques like Lyapunov and G-shaping to minimize the H∞ norm of the closed-loop system.
• Simulation results demonstrate improved performance, achieving stable platooning at reduced time gaps and enhanced robustness to delays.

Introduction

The paper "Multi-Objective $H_{\infty}$ Control for String Stability of Cooperative Adaptive Cruise Control Systems" presents a comprehensive paper on the enhancement of cooperative adaptive cruise control (CACC) systems through the application of a multi-objective $H_{\infty}$ control strategy. This research addresses the critical challenge of achieving string stability in vehicle platoons, particularly when vehicles operate with reduced inter-vehicle spacing to increase road capacity.

Research Objective

The primary objective of this research is to formulate a multi-objective $H_{\infty}$ control approach that guarantees string stability for Adaptive Cruise Control (ACC) and Cooperative Adaptive Cruise Control (CACC) systems. The proposed method distinguishes itself from traditional $H_{\infty}$ control by not only ensuring system stability but also explicitly incorporating string stability into the controller design. String stability, a key aspect for the practical deployment of autonomous platoons, is defined in this context as the non-amplification of disturbances across a vehicle string.

Problem Formulation and Control Design

Key components of the control problem include:

• String Stability Requirement: The string stability condition is expressed using the $H_{\infty}$ norm, ensuring that the perturbation across the vehicle string does not amplify beyond a unit gain.
• Decentralized Control Structure: The control architecture employs a decentralized design, crucial for real-world applicability where each vehicle computes its control inputs without centralized coordination.
• Spacing Policies and Longitudinal Vehicle Dynamics: The paper explores various spacing policies, opting for a constant time-gap policy that optimizes traffic capacity given the dynamics constraints.

The methodology pivots on defining an optimization problem where the controller minimizes the $H_{\infty}$ norm of the closed-loop system subject to conditions ensuring both system and string stability. The solution procedure involves notable techniques such as Lyapunov shaping and G-shaping.

Simulation and Analysis

Simulation studies form the crux of this research, providing performance evaluation under varying conditions. The results demonstrate:

• String Stability Achieved: Under the proposed control strategy, the simulations confirm that both ACC and CACC systems maintain string stability at reduced time gaps (1 second for ACC and 0.5 seconds for CACC), surpassing previously established thresholds.
• Robustness to Delays: The designed controllers exhibit robustness under realistic scenarios with communication and actuator delays, essential for practical applications.
• Comparison with Traditional Controllers: The research evidences significant improvements over conventional control strategies, particularly in decreasing the time-headway required for stable platooning.

Implications and Future Directions

The implications of achieving enhanced string stability through multi-objective $H_{\infty}$ control extend to several areas:

• Traffic Flow Optimization: By allowing smaller inter-vehicle gaps without sacrificing stability, the proposed method facilitates higher traffic throughput and potential congestion alleviation.
• Scalability for Autonomous Systems: The decentralized nature of the control design supports scalable implementations in real-world traffic environments.
• Impact on Safety and Comfort: Improved string stability directly correlates with reduced oscillations in vehicle speed and more predictable vehicle interactions, enhancing both safety and passenger comfort.

Future research avenues may include the exploration of more complex inter-vehicle communication architectures, incorporating non-linear vehicle dynamics, and addressing more intricate traffic scenarios, such as lane changes and intersections.

Conclusion

The paper makes a significant contribution to the domain of vehicular systems control by tailoring a multi-objective $H_{\infty}$ approach to the specific requirements of ACC and CACC systems, thus setting a foundation for future advancements in autonomous vehicle technology. The demonstrated ability to achieve string stability with reduced spacing positions this research as a critical enabler for the deployment of efficient and safe vehicle platoons.