Lyapunov stability-based optimal control of following vehicles on a highway

The application of modern control methods to automated driving of following vehicles on a highway can make the advanced transportation systems much more safe and efficient. This paper focuses on a computational approach to optimal control and stability analysis of the adjacent vehicles following in a single traffic lane of a highway in order to ensure the functional safety and assistance of automated driving systems. These vehicles are 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 responses automatically without intervention from humans (i.e. drivers). To meet such requirements for driving safety, this paper explores a new approach to string stability of following vehicles that travel in a straight line of a highway, using optimal control and Lyapunov stability theories. Consequently, 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 then formulated as a convex optimisation problem in terms of a linear invariant system towards a quadratic optimal criterion. The analysis of these methods for minimising the performance criterion is also given. Finally, the paper ends with a conclusion and perspective for future work.