New Mathematical Tools for Analysis and Control of Platoons of Cars in Future Automated Highway Systems

This paper introduces new mathematical tools for stabilization and asymptotic following in infinite platoons of vehicles in future automated highway systems. The platoon description, behavior analysis and control is approached in 2-D polynomial framework, that is, the dynamics of the problem are described using a fraction of two bivariate polynomials. In contrast to some previous works, the platoon here assumes a leader (and an infinite number of followers), therefore the often used bilateral z-transform should not be used here since it was developed for doubly infinite vehicular strings. The unilateral z-transform seems better suited. However, it brings about the need to take the boundary conditions into consideration; among other, the leader vehicle comes into the scene. The necessary formalism is introduced in the paper and used to provide elegant alternative proofs of some well-known facts about the platooning problem.