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Conference Papers Year : 2013

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

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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Dates and versions

hal-00935300 , version 1 (23-01-2014)

Identifiers

  • HAL Id : hal-00935300 , version 1

Cite

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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