相关论文: Analysis of Lyapunov Method for Control of Quantum…
We present detailed analysis of the convergence properties and effectiveness of Lyapunov control design for bilinear Hamiltonian quantum systems based on the application of LaSalle's invariance principle and stability analysis from…
The condition of a quantum Lyapunov-based control which can be well used in a closed quantum system is that the method can make the system convergent but not just stable. In the convergence study of the quantum Lyapunov control, two…
The convergence of closed quantum systems in the degenerate cases to the desired target state by using the quantum Lyapunov control based on the average value of an imaginary mechanical quantity is studied. On the basis of the existing…
A Lyapunov-based method is presented for stabilizing and controlling of closed quantum systems. The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite…
The finite-time control problem of quantum systems is investigated in this paper. We first define finite-time stability and present a finite-time Lyapunov stability criterion for finite-dimensional quantum systems in coherence vector…
Quantum Lyapunov control was developed in order to transform a quantum system from arbitrary initial states to a target state. The idea is to find control fields that steer the Lyapunov function to zero as $t\rightarrow \infty$, meanwhile…
The natural trajectory tracking problem is studied for generic quantum states represented by density operators. A control design based on the Hilbert-Schmidt distance as a Lyapunov function is considered. The control dynamics is redefined…
In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In analog to the classical probability measure for Markovian processes, we show that the set of invariant…
Rapid state control of quantum systems is significant in reducing the influence of relaxation or decoherence caused by the environment and enhancing the capability in dealing with uncertainties in the model and control process. Bang-bang…
A Lyapunov-based control design for natural trajectory-tracking problems is analyzed for quantum states where the analysis in the generic case is not applicable. Using dynamical systems tools we show almost global asymptotic stability for…
A quantum system whose internal Hamiltonian is not strongly regular or/and control Hamiltonians are not full connected, are thought to be in the degenerate cases. In this paper, convergence problems of the multi-control Hamiltonians closed…
In the design of complex quantum systems like ion traps for quantum computing, it is usually desired to stabilize a particular system state or make the system state track a desired trajectory. Several control theoretical approaches based on…
In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use…
We develop a model-free framework for stabilizing quantum states using only empirical finite-difference evaluations of a measurement-derived Lyapunov observable. The controller requires no knowledge of the Hamiltonian, dissipative…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
Different ways of modelling quantum control systems, formulating control problems and solving the resulting problems are considered and compared. In particular, we compare the performance of geometric and optimal control, as well as…
We design the controls of physical systems that are faced by uncertainties. The system dynamics are described by random hyperbolic balance laws. The control aims to steer the system to a desired state under uncertainties. We propose a…
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
This paper focuses on the invariance control problem for discrete-time switched nonlinear systems. The proposed approach computes controlled invariant sets in a finite number of iterations and directly yields a partition-based invariance…