An adaptive least-squares collocation radial basis function method for the HJB equation
Document Type
Conference Proceeding
Keywords
Adaptive method, HJB equation, Optimal feedback control, Radial basis functionsA-stability, Adaptive methods, Approximate solution, Backward Euler, Discretization method, Finite difference, Hamilton Jacobi Bellman equation, HJB equations, Least-squares collocation, Novel numerical methods, Numerical results, Optimal feedback control, Radial basis functions, Spatial discretizations, Time discretization, Time step, Adaptive algorithms, Discrete event simulation, Feedback control, Image segmentation, Numerical methods, Optimization, Radial basis function networks, Least squares approximations
Faculty
Faculty of Computing, Health and Science
School
School of Engineering
RAS ID
14864
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.
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Comments
Alwardi , H., Wang, S., Jennings, L., & Richardson, S. J. (2012). An adaptive least-squares collocation radial basis function method for the HJB equation. Proceedings of International Conference on Optimization and Control with Applications (OCA2009). (pp. 305-322 ). Harbin, China. Available here