Efficient robust control of first order scalar conservation laws using semi-analytical solutions

Handle URI:
http://hdl.handle.net/10754/563317
Title:
Efficient robust control of first order scalar conservation laws using semi-analytical solutions
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 initial density control and boundary flow control, as a Linear Program. We then show that this framework can be extended to arbitrary control problems involving the control of subsets of the initial and boundary conditions. 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/MILP. 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.
KAUST Department:
Mechanical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Electrical Engineering Program; Distributed Sensing Systems Laboratory (DSS)
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Discrete and Continuous Dynamical Systems - Series S
Issue Date:
Jan-2014
DOI:
10.3934/dcdss.2014.7.525
Type:
Article
ISSN:
19371632
Appears in Collections:
Articles; Electrical Engineering Program; Mechanical Engineering Program; 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.accessioned2015-08-03T11:45:35Zen
dc.date.available2015-08-03T11:45:35Zen
dc.date.issued2014-01en
dc.identifier.issn19371632en
dc.identifier.doi10.3934/dcdss.2014.7.525en
dc.identifier.urihttp://hdl.handle.net/10754/563317en
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 initial density control and boundary flow control, as a Linear Program. We then show that this framework can be extended to arbitrary control problems involving the control of subsets of the initial and boundary conditions. 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/MILP. 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.en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.subjectDistributed parameter systemsen
dc.subjectInterval linear programmingen
dc.subjectOptimal controlen
dc.subjectRobust controlen
dc.subjectTraffic controlen
dc.titleEfficient robust control of first order scalar conservation laws using semi-analytical solutionsen
dc.typeArticleen
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.journalDiscrete and Continuous Dynamical Systems - Series Sen
kaust.authorClaudel, Christian G.en
kaust.authorLi, Yanningen
kaust.authorCanepa, Edward S.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.