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Conference Paper: Contraction of Riccati flows applied to the convergence analysis of the max-plus curse of dimensionality free method

TitleContraction of Riccati flows applied to the convergence analysis of the max-plus curse of dimensionality free method
Authors
Issue Date2013
Citation
2013 European Control Conference, ECC 2013, 2013, p. 2226-2231 How to Cite?
AbstractMax-plus based methods have been recently explored for solution of first-order Hamilton-Jacobi-Bellman equations by several authors. In particular, 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/(Nτ))+O(√τ) where τ is the time discretization step and N is the number of iterations. Here we use a recently established contraction result of the indefinite Riccati flow in Thompson's metric to show that under different technical assumptions, still covering an important class of problems, the total error incorporating a pruning procedure of error order τ2 is O(e-αNτ) +O(τ) for some α > 0 related to the contraction rate of the indefinite Riccati flow. © 2013 EUCA.
Persistent Identifierhttp://hdl.handle.net/10722/219738

 

DC FieldValueLanguage
dc.contributor.authorQu, Zheng-
dc.date.accessioned2015-09-23T02:57:51Z-
dc.date.available2015-09-23T02:57:51Z-
dc.date.issued2013-
dc.identifier.citation2013 European Control Conference, ECC 2013, 2013, p. 2226-2231-
dc.identifier.urihttp://hdl.handle.net/10722/219738-
dc.description.abstractMax-plus based methods have been recently explored for solution of first-order Hamilton-Jacobi-Bellman equations by several authors. In particular, 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/(Nτ))+O(√τ) where τ is the time discretization step and N is the number of iterations. Here we use a recently established contraction result of the indefinite Riccati flow in Thompson's metric to show that under different technical assumptions, still covering an important class of problems, the total error incorporating a pruning procedure of error order τ2 is O(e-αNτ) +O(τ) for some α > 0 related to the contraction rate of the indefinite Riccati flow. © 2013 EUCA.-
dc.languageeng-
dc.relation.ispartof2013 European Control Conference, ECC 2013-
dc.titleContraction of Riccati flows applied to the convergence analysis of the max-plus curse of dimensionality free method-
dc.typeConference_Paper-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.scopuseid_2-s2.0-84893284475-
dc.identifier.spage2226-
dc.identifier.epage2231-

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