# American Institute of Mathematical Sciences

September  2015, 35(9): 4439-4453. doi: 10.3934/dcds.2015.35.4439

## Dynamic programming using radial basis functions

 1 Center for Mathematics, Technische Universität München, 85747 Garching bei München, Germany, Germany

Received  May 2014 Revised  October 2014 Published  April 2015

We propose a discretization of the optimality principle in dynamic programming based on radial basis functions and Shepard's moving least squares approximation method. We prove convergence of the value iteration scheme, derive a statement about the stability region of the closed loop system using the corresponding approximate optimal feedback law and present several numerical experiments.
Citation: Oliver Junge, Alex Schreiber. Dynamic programming using radial basis functions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4439-4453. doi: 10.3934/dcds.2015.35.4439
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