Scaling and Balancing for High-Performance Computation of Optimal Controls

TL;DR

This paper introduces a balancing technique that significantly improves the computational efficiency of optimal control algorithms, demonstrating practical benefits in aerospace applications and cautioning against certain auto-scaling methods.

Contribution

It presents a novel balancing method for optimal control problems that enhances computational efficiency and is applicable across various algorithms and software.

Findings

Balancing improves optimal control computation speed.

Non-canonical scaling can reduce problem difficulty.

Auto-scaling procedures may be counterproductive.

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 non-canonical 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 DoD. A surprising aspect of our analysis shows that it may be inadvisable to use auto-scaling 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.