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

Zheng Qu 1, 2
2 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : McEneaney introduced a curse-of-dimensionality free method for solving HJB equations in which the Hamiltonian is a maximum of linear/quadratic forms. The approximation error was shown to be $O(1/(N\tau))$+$O(\sqrt{\tau})$ where $\tau$ is the time discretization size and $N$ is the number of iterations. Here we use a recently established contraction result for the indefinite Riccati flow in Thompson's metric to show that under different technical assumptions, the error is only of $O(e^{-N\tau})+O(\tau)$.
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https://hal.inria.fr/hal-00935300
Contributor : Zheng Qu <>
Submitted on : Thursday, January 23, 2014 - 12:49:22 PM
Last modification on : Thursday, March 5, 2020 - 6:23:48 PM

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  • HAL Id : hal-00935300, version 1

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Zheng Qu. Contraction of Riccati flows applied to the convergence analysis of a max-plus curse of dimensionality free method. SIAM conference on control and its applications, Jul 2013, San diego, United States. ⟨hal-00935300⟩

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