# On Numerical Algorithm and Interactive Visualization for Optimal Control Problems

L. Grüne, M . Metscher, M. Ohlberger:
**On Numerical Algorithm and Interactive Visualization for Optimal Control Problems**

*Computing and Visualization in Science*
**1**
(4),
221 - 229,
1999

DOI:
10.1007/s007910050020

Keywords: algorithm; visualization; optimal control; dynamic programming; optimal solution trajectories

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## Abstract:

We present methods for the visualization of the numerical solution of optimal control problems. The solution is based on dynamic programming techniques where the corresponding optimal value function is approximated on an adaptively refined grid. This approximation is then used in order to compute approximately optimal solution trajectories. We discuss requirements for the efficient visualization of both the optimal value functions and the optimal trajectories and develop graphic routines that in particular support adaptive, hierarchical grid structures, interactivity and animation. Several implementational aspects using the Graphics Programming Environment 'GRAPE' are discussed.