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Article: Contraction of riccati flows applied to the convergence analysis of a max-plus curse-of-dimensionality-free method
Title | Contraction of riccati flows applied to the convergence analysis of a max-plus curse-of-dimensionality-free method |
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Authors | |
Keywords | Switching linear quadratic control Indefinite Riccati flow Contraction mapping in thompson's part metric Dynamic programming Max-plus basis numerical method |
Issue Date | 2014 |
Publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/sicon.php |
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 Identifier | http://hdl.handle.net/10722/219383 |
ISSN | 2023 Impact Factor: 2.2 2023 SCImago Journal Rankings: 1.565 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Qu, Zheng | - |
dc.date.accessioned | 2015-09-23T02:56:56Z | - |
dc.date.available | 2015-09-23T02:56:56Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | SIAM Journal on Control and Optimization, 2014, v. 52, n. 5, p. 2677-2706 | - |
dc.identifier.issn | 0363-0129 | - |
dc.identifier.uri | http://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.language | eng | - |
dc.publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/sicon.php | - |
dc.relation.ispartof | SIAM Journal on Control and Optimization | - |
dc.subject | Switching linear quadratic control | - |
dc.subject | Indefinite Riccati flow | - |
dc.subject | Contraction mapping in thompson's part metric | - |
dc.subject | Dynamic programming | - |
dc.subject | Max-plus basis numerical method | - |
dc.title | Contraction of riccati flows applied to the convergence analysis of a max-plus curse-of-dimensionality-free method | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/130906702 | - |
dc.identifier.scopus | eid_2-s2.0-84911172040 | - |
dc.identifier.volume | 52 | - |
dc.identifier.issue | 5 | - |
dc.identifier.spage | 2677 | - |
dc.identifier.epage | 2706 | - |
dc.identifier.isi | WOS:000344748000001 | - |
dc.identifier.issnl | 0363-0129 | - |