Cruise Controller Design and Traffic Fluids

We are in times that witness the dawn of a new science: the science of automated vehicle traffic. Although fully automated vehicles are still rare in our roads, we are in a position to find and predict the laws and equations of this new science. The foundations of the new science are built with the help of many areas in mathematics, like Theory of Partial Differential Equations, Numerical Analysis, Dynamical Systems, Fluid Mechanics, Mathematical Physics but above all Nonlinear Control Theory. It is perhaps the first time that Control Theory plays such an important role in the formulation of a new scientific field. This talk shows how solutions of the challenging design problem of cruise controllers (with the help of Lyapunov functions) can allow the derivation of novel macroscopic fluid-like models that describe automated vehicle traffic. The controller parameters determine the physical properties of the traffic fluid which can be very different of the properties of real fluids. Differences and similarities with the science of conventional traffic with human drivers are pointed out. The talk will provide lists of recent results and open problems that need to be studied further. This is a joint work with Dionysis Theodosis and Markos Papageorgiou.