Global Exponential Stabilization of Acyclic Traffic Networks

TL;DR

This paper develops explicit feedback control laws to ensure robust, global, exponential stabilization of uncertain acyclic traffic networks in discrete time, using vector-Lyapunov functions and network acyclicity.

Contribution

It introduces a novel control design method for uncertain traffic networks, proving the necessity of acyclicity for stabilization, with practical application examples.

Findings

Controllers guarantee exponential stability under weak assumptions.

Acyclicity is necessary for stabilization.

Method applicable to realistic traffic networks.

Abstract

This work is devoted to the construction of explicit feedback control laws for the robust, global, exponential stabilization of general, uncertain, discrete-time, acyclic traffic networks. We consider discrete-time, uncertain network models which satisfy very weak assumptions. The construction of the controllers and the rigorous proof of the robust, global, exponential stability for the closed-loop system are based on recently proposed vector-Lyapunov function criteria, as well as the fact that the network is acyclic. It is shown, in this study, that the latter requirement is necessary for the existence of a robust, global, exponential stabilizer of the desired uncongested equilibrium point of the network. An illustrative example demonstrates the applicability of the obtained results to realistic traffic flow networks.