Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

Yanning Li, Edward S. Canepa, Christian Claudel

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.
Original languageEnglish (US)
Pages (from-to)28-39
Number of pages12
JournalIEEE Transactions on Control of Network Systems
Volume1
Issue number1
DOIs
StatePublished - Mar 2014

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