  Alignment control in gravitational-wave detectors has consistently proven to
be a difficult problem due to the stringent noise contamination requirement for
the gravitational wave readout and the radiation-pressure-induced angular
instability in Fabry-Perot cavities (Sidles-Sigg instability). We present the
analysis of a dual-carrier control scheme that uses radiation pressure to
control a suspended mirror, trapping it in the longitudinal degree of freedom
and one angular degree of freedom. We show that this scheme can control the
Sidles-Sigg angular instability. Its limiting fundamental noise source is the
quantum radiation pressure noise, providing an advantage compared to the
conventional angular control schemes. In the Appendix we also derive an exact
expression for the optical spring constant used in the control scheme.
