A Framework for Approximating Perturbed Optimal Control Problems

TL;DR

This paper introduces a framework that uses post-optimality sensitivity information to quickly approximate optimal control trajectories under parameter uncertainty, enabling real-time adjustments without recalculating from scratch.

Contribution

The proposed method provides a novel approach for rapid trajectory adjustment in uncertain environments by leveraging precomputed sensitivity data, reducing computational demands during transit.

Findings

Enables real-time trajectory adjustments with minimal computation.

Reduces the need for in-transit recalculations of optimal control.

Improves robustness of control in uncertain conditions.

Abstract

We consider trajectory optimal control problems in which parameter uncertainty limits the applicability of control trajectories computed prior to travel. Hence, efficient trajectory adjustment is needed to ensure successful travel. However, it is often prohibitive or impossible to recalculate the optimal control in-transit due to strict time constraints or limited onboard computing resources. Thus, we propose a framework for quick and accurate trajectory approximations by using post-optimality sensitivity information. This allows the reduction of uncertain parameter space and an instantaneous approximation of the new optimal controller while using sensitivity data computed and stored pretransit.