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Chinese Control and Decision Conference (CCDC)

Finite-time Target Function Tracking of Quantum Systems with Impulsive Control Fields

Xueming Qian, Baotong Cui

Published May 20, 2023• 0 citations
Publisher

Abstract

In this paper, the finite time tracking issue for a class of closed quantum systems under the action of impulsive control fields is addressed. The aim is to steer the state of the quantum system to the trajectory of a periodic time-varying target. By using the Lyapunov direct method and considering a finite-time control strategy, the modified impulsive tracking controllers are designed such that the error dynamical system converges to zero in finite time. While finite-time tracking implies optimality in convergence time and has better disturbance rejection. Numerical simulations are given to illustrate the effects of system’s trajectory tracking, and also given to demonstrate the superiority of the control laws which are proposed.

DOI
10.1109/ccdc58219.2023.10326529

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In this paper, the finite time tracking issue for a class of closed quantum systems under the action of impulsive control fields is addressed. The aim is to steer the state of the quantum system to the trajectory of a periodic time-varying target. By using the Lyapunov direct method and considering a finite-time control strategy, the modified impulsive tracking controllers are designed such that the error dynamical system converges to zero in finite time. While finite-time tracking implies optimality in convergence time and has better disturbance rejection. Numerical simulations are given to illustrate the effects of system’s trajectory tracking, and also given to demonstrate the superiority of the control laws which are proposed.
Based on model reference adaptive control theory, we design a control law for a given closed quantum system model by means of the Lyapunov stability theorem by choosing a time-varying objective function as the reference model. Meanwhile, the problems of singularities and a very large value of the control fields during the tracking are solved by using an adaptive tracking algorithm. The simulation experiments realize the tracking task from the arbitrary initial states to the time-varying objective function. Under the effect of control law, the state of control system can track from the arbitrary initial state to the state of objective system. Simulation results demonstrate the ability of the control method proposed to adaptively adjust the control laws and real-time track dynamic target system.
Quantum Lyapunov control is a feedback control methodology to determine control fields applied to control quantum systems. In this paper, with the help of the invariant principle of impulsive systems, we investigate the trajectory tracking for quantum systems with impulsive control fields by two Lyapunov functions based on the distance of quantum states and the average value of Hermitian operator which can be regarded as an observable of a quantum system, propose new control fields to drive the quantum systems in the form of sufficient conditions. One numerical simulation is presented to illustrate the effectiveness of the proposed control method.
A control strategy for tracking the trajectory of a time-variant objective function in closed quantum systems is proposed in this paper. The Lyapunov stability theorem is used to design the control law. Meanwhile, the issue of singularity is discussed and the problem of large value of control field occurred during the process of tracking are solved by using an adaptive regulation algorithm of objective function. Simulation results demonstrate the effectiveness and feasibility of the method proposed. We also explore the relationship of effect between control parameters and the error of the control system.
We investigate the Lyapunov control of finite-dimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method.
For quantum state trajectory tracking of density matrix in Liouville equation of quantum systems, with the help of concept in quantum system control, one can apply unitary transformation both to controlled system and free-evolutionary target system such as to change the time-variant and non-stationary target system into a stationary state. Therefore, the quantum state trajectory tracking problem becomes a steering one. State steering control law of the system transformed is designed by means of the Lyapunov stability theorem. Finally, numerical simulation experiments are given for a five-level energy quantum system. The comparison analysis of original system’s trajectory tracking with other method illustrates the advantage in control time of the method proposed.