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Robust bilinear-noise-optimal control for gravitational-wave detectors: A mixed LQG and H∞ approach

Ian A. O. MacMillan* and Lee P. McCuller

  • *Contact author: macmillan@caltech.edu
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Phys. Rev. D 113, 082001 – Published 13 April, 2026

DOI: https://doi.org/10.1103/wm9p-zmxc

Abstract

At its lowest frequencies, LIGO is limited by noise in its many degrees of freedom of suspended optics, which, in turn, introduce noise in the interferometer through their feedback control systems. Nonlinear interactions are a dominant source of low-frequency noise, mixing noise from multiple degrees of freedom. The lowest-order form is bilinear noise, in which the noise from two feedback-controlled subsystems multiplies to mask gravitational waves. Bilinear couplings require control trade-offs that simultaneously balance high- and low-frequency noise. Currently, there is no known lower limit to bilinear control noise. Here, we develop benchmark cost functions for bilinear noise and associated figures of merit. Linear-quadratic-Gaussian (LQG) control then establishes aggressive feedback that saturates the lower bounds on the cost functions. We then develop a mixed LQG and H∞ approach to directly compute stable, robust, and optimal feedback, using the LIGO’s alignment control system as an example. Direct computations are fast while ensuring a global optimum. By calculating optimal robust control, it is possible to construct the lower bound on control noise along the Pareto front of practical controllers for LIGO. This method can be used to drastically improve control noise in existing observatories as well as to set subsystem control noise requirements for next-generation detectors with parametrized design.

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Phys. Rev. D 113, 082001– Published 13 April, 2026
  • Received 12 January 2026
  • Accepted 2 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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