Modelling and Lagrangian control of mixed traffic: platoon coordination, congestion dissipation and state reconstruction

Traffic congestion is a constantly growing problem, with a wide array of negative effects on the society, from wasted time and productivity to elevated air pollution and reduction of safety. The introduction of connected, autonomous vehicles enables a new, Lagrangian paradigm for sensing andcontrolling the traffic, by directly using connected vehicles inside the traffic flow, as opposed to the classical, Eulerian paradigm, which relies on stationary equipment on the road. By using control methods specifically tailored to the Lagrangian paradigm, we are able to influence the traffic flow even if the penetration rate of connected vehicle is low. This allows us to answer one of the central impending questions of the traffic control using emerging technologies: How can we influence the overall traffic by using only a smallportion of vehicles that we can control directly? Traffic phenomena such as moving bottlenecks and stop-and-go waves are particularly pertinent to Lagrangian traffic control, and therefore need to be captured in traffic models. In this thesis we introduce the influence of these phenomena into the cell transmission model, multi-class cell transmission model, and tandem queueing model. We also propose a transition system model based on front tracking, which captures the relevant phenomena, and show under which conditions it corresponds to the Lighthill-Whitham-Richards model. Moving bottlenecks are introduced as a moving zone in which a reduced flux function describes the traffic flow, and their influence on the surrounding traffic is given by solving the Riemann problems at the flux function boundaries. Stop-and-go waves are introduced by constraining the wave speed of rarefaction, resulting in constant stop-and-go wave propagation speed and discharging flow lower than the road capacity, which is consistent with the empirical observations. We use the proposed traffic models to design control laws that address three problems: platoon merging coordination, congestion reduction, and traffic state reconstruction. We study the case when two trucks are closing the distance and merging into a platoon on a public road, and propose an optimal control algorithm which accounts for the mutual influence between the trucks and the surrounding traffic. The proposed control law minimizes the total fuel consumption of the trucks, and improves the reliability of platooning. Then, we consider two forms of the congestion reduction problem: stationary bottleneck d