Iterative Learning Control for Ramp Metering on Service Station On-ramps

TL;DR

An ILC approach based on the Cell Transmission Model with service stations with service stations is proposed, shown that ILC can effectively compensate for potential inaccuracies in model parameter estimates by leveraging historical data.

Abstract

Congestion on highways has become a significant social problem due to the increasing number of vehicles, leading to considerable waste of time and pollution. Regulating the outflow from the Service Station can help alleviate this congestion. Notably, traffic flows follow recurring patterns over days and weeks, allowing for the application of Iterative Learning Control (ILC). Building on these insights, we propose an ILC approach based on the Cell Transmission Model with service stations (CTM-s). It is shown that ILC can effectively compensate for potential inaccuracies in model parameter estimates by leveraging historical data.

Figures (5)

• Figure 1: Illustration of model with one .
• Figure 2: Relations between CTM-s model and MPC formulation. The non-linear dynamics \ref{['eq:demand supply']} - \ref{['eq:D_s controlled']} are relaxed as linear constraints \ref{['ineq:simple merge']}, \ref{['ineq:station merge']} with an extra cost term TTD. Moreover, the variables in blue boxes are known at time step $k$, while those in green boxes are only known after $k+1$. Thus, they are defined as states and inputs, respectively.
• Figure 3: General framework of applying to highway traffic. Yellow and blue boxes denote system $k_0$ and system $k_0+p$ (with horizon length $K$), respectively. We compute the control inputs for system $k_0$ on iteration $d$ by \ref{['modified ILC']} using data of the same system on iteration $d-1$. Then we apply the control inputs until updated at time step $k_0+p$ for the next system.
• Figure 4: Initial upstream demand $D_{-1}(k)$.
• Figure 5: Relative performance of the scheme over $5$ iterations with the scenarios in Table \ref{['tab:r_val']}.