Optimization-based One-side Boundary Control of LWR Traffic Models

TL;DR

This paper develops an optimization-based boundary control method for one-dimensional macroscopic traffic flow models, ensuring stability and invariance through a convex optimization approach.

Contribution

It introduces a unified control framework combining Lyapunov and barrier functionals for traffic models, with conditions for optimal control existence.

Findings

Simulation results demonstrate effective traffic flow stabilization.

The proposed method guarantees both stability and invariance.

Conditions for the existence of optimal boundary controls are established.

Abstract

In this paper, we study the feasibility of a class of optimization-based boundary control of one-dimensional macroscopic traffic flow models, where stability and invariance are achieved by a single boundary control. We define the sets of controllers to stabilize the system to a desired state via Lyapunov functionals, and to ensure forward invariance of a desired subset via boundary control barrier functionals. The control input is then selected from the intersection of those sets via a convex optimization problem. We determine sufficient conditions to ensure the existence of an optimal boundary control problem achieving both stability and invariance for a generic traffic flux function. Simulation results showcase the behavior of the proposed optimization-based controller applied to conservation laws with several traffic flow functions.