Efficient Numerical Optimal Control for Highly Oscillatory Systems

TL;DR

This paper introduces an efficient transcription method for highly oscillatory optimal control problems, significantly reducing computational complexity by approximating slow dynamics and enabling large integration steps, demonstrated on satellite orbit transfer.

Contribution

The paper develops a semi-explicit differential-algebraic equation approach and control regularization technique to efficiently solve highly oscillatory optimal control problems, reducing nonlinear program size.

Findings

Reduced nonlinear program size by over an order of magnitude.

Successfully applied to fuel-optimal low-thrust satellite orbit transfer.

Enabled larger integration steps for oscillatory systems.

Abstract

We present an efficient transcription method for highly oscillatory optimal control problems. For these problems, the optimal state trajectory consists of fast oscillations that change slowly over the time horizon. Out of a large number of oscillations, we only simulate a subset to approximate the slow change by constructing a semi-explicit differential-algebraic equation that can be integrated with integration steps much larger than one period. For the solution of optimal control problems with direct methods, we provide a way to parametrize and regularize the controls. Finally, we utilize the method to find a fuel-optimal orbit transfer of a low-thrust satellite. Using the novel method, we reduce the size of the resulting nonlinear program by more than one order of magnitude.