574 RWTH Publication No: 855790        2022       
TITLE Lyapunov stabilization for nonlocal traffic flow models
AUTHORS Jan Friedrich, Simone Göttlich, Michael Herty
ABSTRACT Using a nonlocal second-order traffic flow model we present an approach to control the dynamics towards a steady state. The system is controlled by the leading vehicle driving at a prescribed velocity and also determines the steady state. Thereby, we consider both, the microscopic and macroscopic scales. We show that the fixed point of the microscopic traffic flow model is asymptotically stable for any kernel function. Then, we present Lyapunov functions for both, the microscopic and macroscopic scale, and compute the explicit rates at which the vehicles influenced by the nonlocal term tend towards the stationary solution. We obtain the stabilization effect for a constant kernel function and arbitrary initial data or concave kernels and monotone initial data. Numerical examples demonstrate the theoretical results.
KEYWORDS Lyapunov stabilization, nonlocal models, microscopic traffic flow
DOI 10.1137/22M152181
PUBLICATION SIAM Journal on Control and Optimization
Vol. 61, Iss. 5 (2023)