  The Vera C. Rubin Observatory is a unique facility for survey astronomy that
will soon be commissioned and begin operations. Crucial to many of its
scientific goals is the achievement of sustained high image quality, limited
only by the seeing at the site. This will be maintained through an Active
Optics System (AOS) that controls optical element misalignments and corrects
mirror figure error to minimize aberrations caused by both thermal and
gravitational distortions. However, the large number of adjustment degrees of
freedom available on the Rubin Observatory introduces a range of degeneracies,
including many that are \textit{noise-induced} due to imperfect measurement of
the wavefront errors. We present a structured methodology for identifying these
degeneracies through an analysis of image noise level. We also present a novel
scaling strategy based on Truncated Singular Value Decomposition (TSVD) that
mitigates the degeneracy, and optimally distributes the adjustment over the
available degrees of freedom. Our approach ensures the attainment of optimal
image quality, while avoiding excursions around the noise-induced subspace of
degeneracies, marking a significant improvement over the previous techniques
adopted for Rubin, which were based on an Optimal Integral Controller (OIC).
This new approach is likely to also yield significant benefits for all
telescopes that incorporate large numbers of degrees of freedom of adjustment.
