Scaling and Balancing for High-Performance Computation of Optimal Controls

Abstract

It is well known that proper scaling can increase the efficiency of computational problems. In this paper, we define and show that a balancing technique can substantially improve the computational efficiency of optimal-control algorithms. We also show that noncanonical scaling and balancing procedures may be used quite effectively to reduce the computational difficulty of some hard problems. These results have been used successfully for several flight and field operations at NASA and the U.S. Department of Defense. A surprising aspect of our analysis shows that it may be inadvisable to use autoscaling procedures employed in some software packages. The new results are agnostic to the specifics of the computational method; hence, they can be used to enhance the utility of any existing algorithm or software.