Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks
Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionElectrical Engineering Program
Mechanical Engineering Program
Date
2014-03Permanent link to this record
http://hdl.handle.net/10754/594249
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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.Citation
Li Y, Canepa E, Claudel C (2014) Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks. IEEE Trans Control Netw Syst 1: 28–39. Available: http://dx.doi.org/10.1109/tcns.2014.2304152.ae974a485f413a2113503eed53cd6c53
10.1109/tcns.2014.2304152