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Frequency Locking of an Optical Cavity Using a Time-Varying Kalman Filtering Approach

The cavity frequency locking problem, which arises in the field of quantum optics, involves matching the resonant frequency of an optical cavity to that of an incoming laser. Although this problem is investigated using linear control techniques for small perturbations, in this brief, we address the nonlinear control problem of frequency locking an optical cavity. Models of the measurement nonlinearities inherent in optical cavities are derived using a singular perturbation approach and instantaneous bounds are placed on the observation errors. A convex set within which the error between the laser frequency and the cavity resonant frequency lies is then determined at each time step by solving two high-order polynomial equations. Based on a reduced-order model of the cavity, a time-varying Kalman filter is designed and simulation results are presented to validate our controller on a full-model of the cavity in the nonlinear region of operation.