A time-varying Kalman filter approach to integral LQG frequency locking of an optical cavity

In this paper, we address the problem of frequency locking an optical cavity which arises in the field of quantum optics. The cavity frequency locking problem involves matching the resonant frequency of an optical cavity to that of an incoming laser beam. We model the measurement nonlinearity inherent in the optical cavity and place instantaneous bounds on the observation errors. A convex set within which the error between the laser frequency and the cavity resonant frequency lies is determined and we synthesize a time-varying integral LQG controller which uses information from this set. Simulation results are shown to validate our design in the nonlinear region of operation.