Exact solutions to robust control problems involving scalar hyperbolic conservation laws using Mixed Integer Linear Programming

Handle URI:
http://hdl.handle.net/10754/575817
Title:
Exact solutions to robust control problems involving scalar hyperbolic conservation laws using Mixed Integer Linear Programming
Authors:
Li, Yanning; Canepa, Edward S. ( 0000-0002-5779-2059 ) ; Claudel, Christian G. ( 0000-0003-0702-6548 )
Abstract:
This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.
KAUST Department:
Mechanical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Electrical Engineering Program; Distributed Sensing Systems Laboratory (DSS)
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Conference/Event name:
51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013
Issue Date:
Oct-2013
DOI:
10.1109/Allerton.2013.6736563
Type:
Conference Paper
ISBN:
9781479934096
Appears in Collections:
Conference Papers; Electrical Engineering Program; Electrical Engineering Program; Mechanical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLi, Yanningen
dc.contributor.authorCanepa, Edward S.en
dc.contributor.authorClaudel, Christian G.en
dc.date.accessioned2015-08-24T09:27:00Zen
dc.date.available2015-08-24T09:27:00Zen
dc.date.issued2013-10en
dc.identifier.isbn9781479934096en
dc.identifier.doi10.1109/Allerton.2013.6736563en
dc.identifier.urihttp://hdl.handle.net/10754/575817en
dc.description.abstractThis article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.titleExact solutions to robust control problems involving scalar hyperbolic conservation laws using Mixed Integer Linear Programmingen
dc.typeConference Paperen
dc.contributor.departmentMechanical Engineering Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentElectrical Engineering Programen
dc.contributor.departmentDistributed Sensing Systems Laboratory (DSS)en
dc.identifier.journal2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)en
dc.conference.date2 October 2013 through 4 October 2013en
dc.conference.name51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013en
dc.conference.locationMonticello, ILen
kaust.authorClaudel, Christian G.en
kaust.authorLi, Yanningen
kaust.authorCanepa, Edward S.en
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