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

Authors:
H. Alwardi;S. Wang;L. S. Jennings
Affiliations:
Department of Mathematics, Nizwa College of Applied Sciences, Nizwa, Sultanate of Oman 611;School of Mathematics & Statistics, The University of Western Australia, Crawley, Australia 6009;School of Mathematics & Statistics, The University of Western Australia, Crawley, Australia 6009
Venue:
Journal of Global Optimization
Year:
2013

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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.