Tracking control laws for some quantum systems based on nonlinear dynamic inversion method

Since real-valued equations of quantum systems are equivalent to the Schrödinger equation, they can provide a convenient way for theoretical analysis and control design, and finally they can assist in the implementation of quantum control, this paper aims at design tracking control laws for some quantum systems based on Nonlinear Dynamic Inversion method in the case that quantum systems are modeled by the real-valued equations. Firstly, the real-valued equations are given for two-level and three level quantum systems. Secondly, after the characteristics of the quantum system models are thoroughly analyzed, the tracking controllers are designed for these quantum systems based on Nonlinear Dynamic Inversion method, and the exponential convergence of the control system is proved. Finally, simulation studies are made to show how to achieve state transfer and how the states track their goal states by the designed controllers; the convergence and validity of the control systems are also illustrated.