Stability Analysis of Following Vehicles on a Highway for Safety of Automated Transportation Systems

The development and integration of advanced control technologies in vehicles and infrastructure can make intelligent (or automated) transportation systems much more safe and efficient. This paper focuses on a proper approach to stability and control of two adjacent vehicles following each other on the same traffic lane of a highway to ensure the functional safety of their automated driving systems. These vehicles are as entirely automated as they have the ability to follow a line path at a high speed and reduce the distance that separates them while adjusting their dynamic responses automatically without intervention from humans (i.e. drivers). To meet requirements for driving safety and stability, this paper explores a new approach to string stability of (any) two adjacent vehicles traveling in the same direction based on using optimal control and Lyapunov stability theories. Therefore, sufficient conditions for string stability of a vehicle traffic using continuous-time Lyapunov function and matrix Riccati equation are presented. The search for a quadratic Lyapunov function is formulated as a convex optimization problem in terms of a linear invariant system towards a quadratic optimal criterion. The analysis of these methods for minimizing the desired performance criteria is also given. Finally, the paper ends with a conclusion and perspective for future work.