M. Rungger and O. Stursberg, “Function Approximation for the Deterministic Hamilton-Jacobi-Bellman Equation,” in Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on, IEEE, Ed. Shanghai, China: IEEE, 2009, pp. 2268–2273.


Based on Gaussian basis functions, a new method for calculating the Hamilton-Jacobi-Bellman equation for deterministic continuous-time and continuous-valued optimal control problems is proposed. A semi-Lagrangian discretization scheme is used to obtain a discrete-time finite-state approximation of the continuous dynamics. The value function of the discretized system is approximated by a Gaussian network. Limit behavior analysis provides a proof of convergence for the scheme. The performance of the presented approach is demonstrated for an underpowered inverted pendulum as numerical example. Furthermore, a comparison to the approximation by continuous piecewise affine functions (the current state of the art) shows the benefits of the approximation technique proposed here.



  author = {M. Rungger and O. Stursberg},
  title = {{Function Approximation for the Deterministic Hamilton-Jacobi-Bellman Equation}},
  booktitle = {48th IEEE Conference on Decision and Control},
  year = {2009},
  pages = {2268-2273},
  comment = {ISBN: 978-1-4244-3872-3, 26 Normseiten}