Controller design for heterogeneous traffic with bottleneck and disturbances

This paper studies an optimal tuning of the boundary controller for a heterogeneous traffic flow model with disturbances in order to alleviate congested traffic. The macroscopic first-order N-class Aw-Rascle traffic model consists of 2N hyperbolic partial differential equations. The vehicle size and the driver's behavior characterize the type of vehicle. There are m positive characteristic velocities and 2N - m negative characteristic velocities in the congested traffic after linearizing the model equations around the steady state depending on the spatial variable. By using the backstepping method, a controller implemented by a ramp metering at the inlet boundary is designed for rejecting the disturbances to stabilize the 2N x 2N heterogeneous traffic system. The developed controller in terms of proportional integral control is derived from mapping the original system to a target system with a proportional integral boundary control rejecting the disturbances. The integral input-to-state stability of the target system is proved by using the Lyapunov method. Finally, an optimization problem is established and solved for seeking the optimal tuning of the controller. (c) 2022 Elsevier Ltd. All rights reserved.