An adaptive least-squares collocation radial basis function method for the HJB equation

Authors:
H. Alwardi;S. Wang;L. S. Jennings;S. Richardson
Affiliations:
Department of Mathematics, Nizwa College of Applied Sciences, Nizwa, Sultanate of Oman 611;School of Mathematics and Statistics, The University of Western Australia, Crawley, Australia 6009;School of Mathematics and Statistics, The University of Western Australia, Crawley, Australia 6009;School of Engineering, Edith Cowan University, Joondalup, Australia 6027
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

We present a novel numerical method for the Hamilton---Jacobi---Bellman equation governing a class of optimal feedback control problems. The spatial discretization is based on a least-squares collocation Radial Basis Function method and the time discretization is the backward Euler finite difference. A stability analysis is performed for the discretization method. An adaptive algorithm is proposed so that at each time step, the approximate solution can be constructed recursively and optimally. Numerical results are presented to demonstrate the efficiency and accuracy of the method.