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Article: Contraction of riccati flows applied to the convergence analysis of a max-plus curse-of-dimensionality-free method

TitleContraction of riccati flows applied to the convergence analysis of a max-plus curse-of-dimensionality-free method
Authors
KeywordsSwitching linear quadratic control
Indefinite Riccati flow
Contraction mapping in thompson's part metric
Dynamic programming
Max-plus basis numerical method
Issue Date2014
Citation
SIAM Journal on Control and Optimization, 2014, v. 52, n. 5, p. 2677-2706 How to Cite?
Abstract© 2014 Society for Industrial and Applied Mathematics Max-plus based methods have been recently explored for solution of first-order Hamilton-Jacobi-Bellman equations by several authors. Among several max-plus numerical methods, McEneaney's curse-of-dimensionality-free method applies to the equations where the Hamiltonian takes the form of a (pointwise) maximum of linear/quadratic forms. In previous works of McEneaney and Kluberg, the approximation error of the method was shown to be O (1/(NT))+ O(√t), where T is the time discretization step and N is the number of iterations. Here we use a recently established contraction result for the indefinite Riccati flow in Thompson's part metric to show that under different technical assumptions, still covering an important class of problems, the error is only of order O (e-αN T ) + O (T) for some α > 0. This also allows us to obtain improved estimates of the execution time and to tune the precision of the pruning procedure, which in practice is a critical element of the method.
Persistent Identifierhttp://hdl.handle.net/10722/219383
ISSN
2015 Impact Factor: 1.491
2015 SCImago Journal Rankings: 1.904

 

DC FieldValueLanguage
dc.contributor.authorQu, Zheng-
dc.date.accessioned2015-09-23T02:56:56Z-
dc.date.available2015-09-23T02:56:56Z-
dc.date.issued2014-
dc.identifier.citationSIAM Journal on Control and Optimization, 2014, v. 52, n. 5, p. 2677-2706-
dc.identifier.issn0363-0129-
dc.identifier.urihttp://hdl.handle.net/10722/219383-
dc.description.abstract© 2014 Society for Industrial and Applied Mathematics Max-plus based methods have been recently explored for solution of first-order Hamilton-Jacobi-Bellman equations by several authors. Among several max-plus numerical methods, McEneaney's curse-of-dimensionality-free method applies to the equations where the Hamiltonian takes the form of a (pointwise) maximum of linear/quadratic forms. In previous works of McEneaney and Kluberg, the approximation error of the method was shown to be O (1/(NT))+ O(√t), where T is the time discretization step and N is the number of iterations. Here we use a recently established contraction result for the indefinite Riccati flow in Thompson's part metric to show that under different technical assumptions, still covering an important class of problems, the error is only of order O (e-αN T ) + O (T) for some α > 0. This also allows us to obtain improved estimates of the execution time and to tune the precision of the pruning procedure, which in practice is a critical element of the method.-
dc.languageeng-
dc.relation.ispartofSIAM Journal on Control and Optimization-
dc.subjectSwitching linear quadratic control-
dc.subjectIndefinite Riccati flow-
dc.subjectContraction mapping in thompson's part metric-
dc.subjectDynamic programming-
dc.subjectMax-plus basis numerical method-
dc.titleContraction of riccati flows applied to the convergence analysis of a max-plus curse-of-dimensionality-free method-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1137/130906702-
dc.identifier.scopuseid_2-s2.0-84911172040-
dc.identifier.volume52-
dc.identifier.issue5-
dc.identifier.spage2677-
dc.identifier.epage2706-

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