A Review of Pseudospectral Optimal Control: From Theory to Flight

TL;DR

This paper reviews the development and application of pseudospectral optimal control theory, highlighting its theoretical foundations, implementation in NASA spacecraft, and emerging trends in aerospace and autonomous systems.

Contribution

It provides a comprehensive review of pseudospectral optimal control theory, emphasizing its theoretical basis, practical implementation in flight, and recent advancements in the field.

Findings

Successful flight demonstrations onboard NASA spacecraft.

Pseudospectral optimal control is transforming aerospace control solutions.

Emerging techniques are enhancing theory and practice in autonomous systems.

Abstract

The home space for optimal control is a Sobolev space. The home space for pseudospectral theory is also a Sobolev space. It thus seems natural to combine pseudospectral theory with optimal control theory and construct ``pseudospectral optimal control theory,'' a term coined by Ross. In this paper, we review key theoretical results in pseudospectral optimal control that have proven to be critical for a successful flight. Implementation details of flight demonstrations onboard NASA spacecraft are discussed along with emerging trends and techniques in both theory and practice. The 2011 launch of pseudospectral optimal control in embedded platforms is changing the way in which we see solutions to challenging control problems in aerospace and autonomous systems.