Time-Triggered Reduced Desensitization Formulation For Solving Optimal Control Problems

TL;DR

This paper introduces a time-triggered desensitization method for optimal control problems, improving robustness against parameter uncertainties by selectively applying desensitization over specific time intervals.

Contribution

It proposes a novel time-triggered desensitization approach based on the Reduced Desensitization Formulation, enhancing optimality in robust trajectory planning.

Findings

Temporal desensitization achieves similar robustness as full desensitization.

Improved final cost functional with selective desensitization.

Effective for low-thrust rendezvous and orbit-raising maneuvers.

Abstract

Fuel-optimal trajectories are inherently sensitive to variations in model parameters, such as propulsion system thrust magnitude. This inherent sensitivity can lead to dispersions in cost-functional values, when model parameters have uncertainties. Desensitized optimal control aims at generating robust optimal solutions while taking into account uncertainties in the model parameters. While desensitization techniques typically apply along the entire flight time, this paper introduces a novel time-triggered desensitization mechanism by modifying a recently developed desensitization method -- the Reduced Desensitization Formulation (RDF). By selectively desensitizing over specific time intervals of trajectories, we demonstrate the improved optimality of desensitized trajectories. We investigate the effects of temporal desensitization on the final cost and trajectory by considering thrust magnitude uncertainty for two classes of low-thrust trajectory optimization problems: 1) minimum-fuel rendezvous maneuvers and 2) orbit-raising maneuvers. Results show that temporal desensitization can achieve similar dispersion levels to full mission desensitization with an improved final cost functional.