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 consists 2N hyperbolic partial differential equations. vehicle size and driver’s behavior characterize type vehicle. There are m positive characteristic velocities 2N−m negative after linearizing equations around steady state depending on spatial variable. By using backstepping method, implemented by ramp metering at inlet is designed rejecting stabilize 2N×2N system. developed terms proportional integral control derived from mapping original system target disturbances. input-to-state stability proved Lyapunov method. Finally, optimization problem established solved seeking controller.