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

Authors: Azzedine Yahiaoui

Addresses: Center for Building & Systems, Eindhoven University of Technology (TU/e), PO Box 513, Den Dolech 2, 5600MB Eindhoven, the Netherlands

Abstract: 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.

Keywords: safe driving of vehicles; control system analysis; matrix Riccati equation; string stability analysis; Lyapunov function.

DOI: 10.1504/IJVAS.2018.10017222

International Journal of Vehicle Autonomous Systems, 2018 Vol.14 No.2, pp.196 - 211

Received: 18 Jul 2017
Accepted: 29 Jul 2018

Published online: 13 Nov 2018 *

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