  The detection of high-frequency gravitational waves around kHz is critical to
understanding the physics of binary neutron star mergers. A new interferometer
design has been proposed in [Phys. Rev. X {\bf 13}, 021019 (2023)], featuring
an L-shaped optical resonator as the arm cavity, which resonantly enhances kHz
gravitational-wave signals. This new configuration has the potential to achieve
better high-frequency sensitivity than the dual-recycled Fabry-Perot Michelson.
In this article, we propose a sensing and control scheme for this
configuration. Despite having the same number of length degrees of freedom as
the dual-recycled Fabry-Perot Michelson, the new configuration requires one
less degree of freedom to be controlled due to the degeneracy of two length
degrees of freedom at low frequencies. We has also shown that introducing the
Schnupp asymmetry is ineffective for controlling the signal-recycling cavity
length. Therefore, we propose adding control fields from the dark port to
control this auxiliary degree of freedom.
