Arguably, highway traffic is one of the main means of transportation in modern megalopolises. The continuously increasing traffic demand has led to severe degradation of the available infrastructure, which manifests itself through, increased travel times, reduced safety, increased discomfort, high fuel consumption, and increased harmful emissions, costing several billion euros every year. Extending the road infrastructure is an obvious solution to this problem, which, however, is rather expensive and, in most cases, virtually not realizable. In contrast, real-time traffic flow control has been proved to be a viable, practically feasible, and low-cost alternative.
Besides being intuitively expected that, on a macroscopic level (i.e. when considering a "population" of vehicles and not each individual vehicle), the traffic flow dynamics may be compared to fluid flows, traffic flow evidently may be quantified utilizing, at each point in time, information from each particular location (e.g. on a highway stretch). For these reasons, continuum (in time and space) dynamical systems, i.e. Partial Differential Equation (PDE) systems, constitute perhaps the most recognizable form of a macroscopic description of the traffic flow dynamics, as they provide not only an accurate and elegant description, but also retain the distributed nature of traffic flow. Exploiting the detailed description of the traffic flow dynamics using PDEs, a new framework is introduced for control and estimation of traffic flow in highways, which capitalizes on PDE control tools and which doesn't rely on model reduction or any discrete approximations (apart, only, from the implementation stage), thus also offering provable stability guarantees.
Specifically, in the new methodology, feedforward and feedback control designs are developed, based on continuum in time and space traffic-flow models, which assign to the traffic flow the desired shape, with an a priori prescribed convergence rate and for any initial traffic profile. In certain cases, the novel control and estimation algorithms employ measurements/actuation only at the entries and exits of the highway, thus requiring minimum amount of information and actuation capabilities. The designs are accompanied with tools for verification that are introduced, which provide quantified actual performance guarantees and robustness margins of the proposed algorithms. The methodologies are validated in simulation, using fictitious and real data of traffic.
