Lyapunov stabilization of a nonlocal LWR traffic flow model

Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity

We consider an extension of the traffic flow model proposed by Lighthill, Whitham and Richards, in which the mean velocity depends on a weighted mean of the downstream traffic density. We prove well-posedness and a regularity result for entropy weak solutions of the corresponding Cauchy problem, and use a finite volume central scheme to compute approximate solutions. We perform numerical tests ...

Heterogeneous Traffic Flow Modelling with the Lwr Model Using Passenger-car Equivalents

SUMMARY This paper presents an extension of Lighthill, Whitham and Richards' dynamic traffic flow model (LWR) to a number of vehicle classes. Each class will be described by a separate fundamental diagram. When the various diagrams are similar in shape a scaling can be carried out that is related to the passenger-car equivalents. We present both an analytical framework and a numerical computati...

Multianticipative Nonlocal Macroscopic Traffic Model

Multianticipative driving behavior, where a vehicle reacts to many vehicles in front, has been extensively studied and modeled using a car-following (i.e., microscopic) approach. A lot of effort has been undertaken to model such multianticipative driving behavior using a macroscopic approach, which is useful for real-time prediction and control applications due to its fast computational demand....

Conservation laws with a nonlocal flow, Application to pedestrian traffic

A Lyapunov characterization of robust stabilization

One of the fundamental facts in control theory (Artstein’s theorem) is the equivalence, for systems affine in controls, between continuous feedback stabilizability to an equilibrium and the existence of smooth control Lyapunov functions. This equivalence breaks down for general nonlinear systems, not affine in controls. One of the main results in this paper establishes that the existence of smo...