Forward Completeness and Applications to Control of Automated Vehicles

TL;DR

This paper introduces a relaxed Lyapunov-like condition for forward completeness in control systems and applies it to design decentralized cruise controllers for automated vehicles, ensuring safety and adaptability in complex driving scenarios.

Contribution

It presents a novel relaxed Lyapunov condition for forward completeness and applies it to develop decentralized, collision-avoiding cruise controllers for automated vehicles.

Findings

Controllers handle variable road widths and ramps.

Decentralized control ensures collision avoidance.

The approach guarantees global solution existence.

Abstract

Forward complete systems are guaranteed to have solutions that exist globally for all positive time. In this paper, a relaxed Lyapunov-like condition for forward completeness is presented for finite-dimensional systems defined on open sets that does not require boundedness of the Lyapunov-like function along the solutions of the system. The corresponding condition is then exploited for the design of autonomous two-dimensional movement, with focus on lane-free cruise controllers for automated vehicles described by the bicycle kinematic model. The derived feedback laws (cruise controllers) are decentralized and can account for collision avoidance, roads of variable width, on-ramps and off-ramps as well as different desired speed for each vehicle.