Clock Steering Techniques for Atomic Clocks of Arbitrary Order

In this paper, we have explored the possibility to exploit control theory to introduce new steering techniques for atomic clocks of arbitrary order. Current studies show that most of the well-known steering methods are developed for the two-state atomic clock model and not much attention is paid to find efficient steering methods for higher-order atomic clocks. We introduce two novel clock steering methods for atomic clocks: one based on output stabilization problem and the other based on frequency deviation regulation problem. First, we prove the existence of control laws for the solvability of these two problems for atomic clocks. Second, to find a suitable control law for both steering problems, we outlined efficient procedures to obtain gain matrices and used the Kalman filter for state estimates. A few numerical examples have been given to analyze the performance of the proposed control approaches.