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An adaptive domain decomposition method for the Hamilton–Jacobi–Bellman equation

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  • H. Alwardi
  • S. Wang
  • L. Jennings

Abstract

In this paper, we propose an efficient algorithm for a Hamilton–Jacobi–Bellman equation governing a class of optimal feedback control and stochastic control problems. This algorithm is based on a non-overlapping domain decomposition method and an adaptive least-squares collocation radial basis function discretization with a novel matrix inversion technique. To demonstrate the efficiency of this method, numerical experiments on test problems with up to three states and two control variables have been performed. The numerical results show that the proposed algorithm is highly parallelizable and its computational cost decreases exponentially as the number of sub-domains increases. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • H. Alwardi & S. Wang & L. Jennings, 2013. "An adaptive domain decomposition method for the Hamilton–Jacobi–Bellman equation," Journal of Global Optimization, Springer, vol. 56(4), pages 1361-1373, August.
  • Handle: RePEc:spr:jglopt:v:56:y:2013:i:4:p:1361-1373
    DOI: 10.1007/s10898-012-9850-2
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    References listed on IDEAS

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    1. Pereyra, V. & Scherer, G., 2006. "Least squares collocation solution of elliptic problems in general regions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(1), pages 226-230.
    2. Antanas Žilinskas, 2010. "On similarities between two models of global optimization: statistical models and radial basis functions," Journal of Global Optimization, Springer, vol. 48(1), pages 173-182, September.
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