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Conference Paper: Contraction of Riccati flows applied to the convergence analysis of the max-plus curse of dimensionality free method
Title | Contraction of Riccati flows applied to the convergence analysis of the max-plus curse of dimensionality free method |
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Authors | |
Issue Date | 2013 |
Citation | 2013 European Control Conference, ECC 2013, 2013, p. 2226-2231 How to Cite? |
Abstract | Max-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 Identifier | http://hdl.handle.net/10722/219738 |
DC Field | Value | Language |
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dc.contributor.author | Qu, Zheng | - |
dc.date.accessioned | 2015-09-23T02:57:51Z | - |
dc.date.available | 2015-09-23T02:57:51Z | - |
dc.date.issued | 2013 | - |
dc.identifier.citation | 2013 European Control Conference, ECC 2013, 2013, p. 2226-2231 | - |
dc.identifier.uri | http://hdl.handle.net/10722/219738 | - |
dc.description.abstract | Max-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.language | eng | - |
dc.relation.ispartof | 2013 European Control Conference, ECC 2013 | - |
dc.title | Contraction of Riccati flows applied to the convergence analysis of the max-plus curse of dimensionality free method | - |
dc.type | Conference_Paper | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.scopus | eid_2-s2.0-84893284475 | - |
dc.identifier.spage | 2226 | - |
dc.identifier.epage | 2231 | - |