Fractional Exponential Feedback Control for Finite-Time Stabilization and Its Application in a Spin-Exchange Relaxation-Free Comagnetometer

This article is the first work to propose a series of control strategies for the longitudinal electron spin polarization of the spin-exchange relaxation-free comagnetometer system to ensure its ultrastable measurement. Two types of finite-time control strategies are presented for a nonlinear system with affine input. The first control strategy is finite-time fractional exponential feedback control (FEFC), which ensures that the trajectories of an autonomous system converge to an equilibrium state in a finite time that can be specified. The second control strategy is finite-time robust FEFC, which provides a finite-time stability of a nonautonomous system with unknown structures under disturbance and perturbations, and its upper bound of the settling time can be estimated. The theoretical results are supported by numerical simulations.

Automated summary

This article proposes a series of control strategies for ensuring the ultrastable measurement of the spin-exchange relaxation-free comagnetometer system, including finite-time fractional exponential feedback control and finite-time robust FEFC.