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) |