Design of control sequence of pulses for the population transfer of high dimensional spin 1/2 quantum systems

On the basis of the relationship between the Hamiltonian of spin 1/2 quantum system under control and the energy level structure and transitions, a radio frequency pulse sequence is designed using intuitive and half counter-intuitive sequences of pulse to transfer the population of the 3-qubit system coherently. The effectiveness of the designed control sequence is verified through the system simulation experiment of the evolution of state. In principle, the design method of the control pulse sequence proposed can be generalized to use in the quantum systems of higher dimension.     

Controllability of Quantum Systems with SU(1, 1) Dynamical Symmetry

This paper presents sufficient and necessary conditions for the propagator controllability of a class of infinite-dimensional quantum systems with SU(1, 1) dynamical symmetry through the isomorphic mapping to the non-unitary representation of SU(1, 1). The authors prove that the elliptic condition of the total Hamiltonian is both necessary and sufficient for the controllability and strong controllability. The obtained results can be also extended to control systems with SO(2, 1) dynamical symmetry.     

An augmented BV setting for feedback switching control

<正> This paper considers dynamical systems under feedback with control actions limited toswitching.The authors wish to understand the closed-loop systems as approximating multi-scale problemsin which the implementation of switching merely acts on a fast scale.Such hybrid dynamicalsystems are extensively studied in the literature,but not much so far for feedback with partial stateobservation.This becomes in particular relevant when the dynamical systems are governed by partialdifferential equations.The authors introduce an augmented BV setting which permits recognition ofcertain fast scale effects and give a corresponding well-posedness result for observations with such minimalregularity.As an application for this setting,the authors show existence of solutions for systemsof semilinear hyperbolic equations under such feedback with pointwise observations.     

基于时域有限差分方法求解薛定谔方程

时域有限差分(finite difference time domain, FDTD)方法广泛应用于电磁场仿真领域,并与量子力学理论相结合来求解时域薛定谔方程,然而数值计算中的稳定性研究缺少理论方面的探讨。基于冯·诺依曼的稳定性分析方法得到了时域薛定谔方程的一维以及多维的稳定性条件,并且讨论了在不同势能情况下该稳定性条件的表现形式。数值结果充分证明了结论的正确性。     

FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS

1 IntroductionIn the last few decades, symplectic geometry becomes a lbcus fOr multi-disciplines. Aspointed out in [1l: '"' cIassical mechanics, statistical mechanics, and quantum mechanics aretreated from the same perspective, that ofsylllplectic geornetry thus showing the unifying powerof the symp1ectic geometric approach." Particularly it becomes a new frame fOr Hamiltoniansystems[2--5]. Symp1ectic a1gorithm, [6] etc., provides a numerical method fOr solving the relatedproblems.In contr…     

分数阶线性系统的能观性研究

在对一类由分数阶线性微分方程描述的系统的能观性问题研究中,通过分数阶线性定常系统求解,给出了分数阶线性定常和时变系统一般解的统一表达式。在给出分数阶系统能观性定义的基础上,提出并证明了分数阶线性系统时变和定常系统能观性的充分和必要条件,以及分数阶线性定常系统的能观性判据,所得结论对分数阶控制系统的分析与综合是有益的。     

Krein space approach to robust H∞ filtering for linear uncertain systems

A novel Krein space approach to robust H ∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then a Krein space approach is used to tackle the robust H ∞ filtering problem. To this end, a new Krein space formal system is designed according to the original sum quadratic constraint (SQC) without introducing any nonzero factors into it and, consequently, the estimate recursion is obtained through the filter gain in Krein space. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.     

EXTENDED CASIMIR APPROACH TO CONTROLLED HAMILTONIAN SYSTEMS

In this paper,we first propose an extended Casimir method for energy-shaping.Then itis used to solve some control problems of Hamiltonian systems.To solve the H_x control problem,theenergy function of a Hamiltonian system is shaped to such a form that could be a candidate solution ofHJI inequality.Next,the energy function is shaped as a candidate of control ISS-Lyapunov function,and then the input-to-state stabilization of port-controlled Hamiltonian systems is achieved.Someeasily verifiable sufficient conditions are presented.     

Optimal Output Tracking Control and Stabilization of Networked Control Systems with Packet Losses

This paper studies the optimal output tracking control and stabilization for networked control systems with packet losses via output feedback control. Both finite-horizon and infinite-horizon cases are considered. For the finite-horizon case, the authors introduce an augmented system according to the state variable and the reference trajectory for the first time. Based on a set of difference Riccati equations, an optimal output feedback tracking controller is proposed by applying the stochastic maximum principle. And an optimal estimator is presented. For the infinite-horizon case, a necessary and sufficient condition for the stabilization of the system is provided. And an optimal output feedback stabilizing tracking controller is obtained by establishing a set of algebraic Riccati equations. Finally,numerical examples are given to verify the proposed results.     

Characteristic polynomial assignment in F-M model Ⅱ of 2-D systems

The problems of characteristic polynomial assignment in Fornasini-Marchesini (F-M) model Ⅱ of 2-D systems are investigated. The corresponding closed-loop systems described by F-M model Ⅱ are obtained via the state feedback.Using the algebraic geometry method, the characteristic polynomial assignment in the closed-loop systems is discussed. In terms of the theory of algebraic geometry, the problem of characteristic polynomial assignment is transferred to the one whether a rational mapping is onto. Sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial in F-M model Ⅱ of 2-D systems via state feedback are derived, and they are available for multi-input cases. It also has been shown that this method can be applied to assign the characteristic polynomial with output feedback. The sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial of multi-input 2-D systems described by F-M model Ⅱ with output feedback are established.     

跳跃机器人模糊自适应轨迹跟踪控制

从受完整约束和非完整约束的腾空相到仅受完整约束的站立相,利用空间浮动基,分阶段建立了类人机器人非规则运动-跳跃运动通用动力学模型;基于Lynapunov方法设计自适应率,研究了跳跃机器人模糊自适应轨迹跟踪控制,保证跟踪收敛和闭环系统的渐进稳定。仿真研究表明,跳跃机器人通用动力学模型为空间机器人建模提供参考;模糊自适应与计算力矩混杂模型轨迹跟踪控制改善了系统自适应性,丰富了非规则运动的姿态控制和稳定性分析方法。     

Constrained predictive control of nonlinear stochastic systems

The receding horizon control (RHC) problem is considered for nonlinear Markov jump systems which can be represented by Takagi-Sugeno fuzzy models subject to constraints both on control inputs and on observe outputs. In the given receding horizon, for each mode sequence of the T-S modeled nonlinear system with Markov jump parameter, the cost function is optimized by constraints on state trajectories, so that the optimization control input sequences are obtained in order to make the state into a terminal invariant set. Out of the receding horizon, the stability is guaranteed by searching a state feedback control law. Based on such stability analysis, a linear matrix inequality approach for designing receding horizon predictive controller for nonlinear systems subject to constraints both on the inputs and on the outputs is developed. The simulation shows the validity of this method.         

Formation Tracking for Nonlinear Multi-agent Systems with Input and Output Quantization via Adaptive Output Feedback Control

Signal quantization can reduce communication burden in multi-agent systems, whereas it brings control challenge to multi-agent formation tracking. This paper studies the output feedback control problem for formation tracking of multi-agent systems with both quantized input and output.The agents are described by a nonlinear dynamic model with unknown parameters and immeasurable states. To estimate immeasurable states and solve the uncertainties, state observers are developed by using dynamic high-gain tools. Through proper parameter designs, an output feedback quantized controller is established based on quantized output signals, and the quantization effect on the control system is eliminated. Stability analysis proves that, with the proposed control scheme, multi-agent systems can track the reference trajectory while forming and maintaining the desired formation shape.In addition, all the signals in the closed-loop systems are bounded. Finally, the numerical simulation and practical experiment are provided to verify the theoretical analysis.     

区间系统状态反馈控制的完整性设计

研究了一类不确定区间系统具有完整性的状态反馈控制设计问题 ,其中不确定性描述为系统状态矩阵的各个元素在一些确定的区间内变化。在给出区间系统的一种等价描述后 ,利用Lyapunov稳定性理论 ,导出了闭环区间系统具有完整性的充分条件 ,给出了相应的状态反馈控制器设计方法及具体设计步骤。最后通过数值算例说明了所提设计方法的有效性。     

Lindblad型开放量子系统最优控制

对于伴随着松弛和耗散的Lindblad型开放量子系统,采用基于Liouville超算符变换的方法,将开放量子系统的动力学微分方程的矩阵表达形式转化成向量表达以简化微分方程的求解。以系统被控状态到达目标状态的期望值为性能指标,对变换后的开放量子系统进行最优控制律的设计,以达到状态转移的目的。在MATLAB环境下以2能级开放量子系统为例进行了系统仿真实验。对控制参数的变化对系统的布居数转移概率及其控制时间的影响进行了对比实验,并对实验结果进行了对比分析。

Abstract：

In order to solve the state of an open quantum system with relaxation and dissipation,the dynamical equation of the system in matrix was transformed into vector form in Liouville space. Taking the expectation value for the state under control reaching the target state as performance indicators,an optimal control function was derived for the system transformed. The control a 2-level open quantum system was simulated on in MATLAB. The influence to population transfer probability and control time caused by changing of parameters were analysed contrastively.     

航天器三维空间追逃问题研究

针对固定时间下的两航天器三维空间追逃问题,采用协同进化算法将复杂的双边最优规划问题简化成对追逃过程中纳什均衡点的搜索,进而得出追逃双方的最优对抗策略及解算方法。考虑在保证算法计算精度的前提下缩短计算时间,将对策模型进行简化处理,以航天器推力指向角为控制量对协同进化算法进行编码设计,利用B样条基函数对编码进行逼近拟合。两航天器均为连续小推力作用,以二者的末端相对距离作为支付函数,逃逸器希望支付最大,追踪器希望支付最小,并依此建立共享适应度函数。所提方法中对协同算子进行改进设计,提高算法空间搜索能力,并采用精英保留策略提高算法的收敛速度。仿真算例得到追逃双方的最优控制策略及相应的追逃轨迹,表明所提方法的能够解决此类航天器追逃问题。     

不确定广义离散系统的鲁棒H-infinity控制

研究E矩阵,确定其它系数矩阵都存在满足范数有界条件的参数不确定性广义离散线性系统的鲁棒H∞控制问题。利用线性矩阵不等式方法,导出广义离散线性系统正则、因果、稳定且传递函数满足给定的范数界的等价条件。在此基础上,可以将广义不确定离散线性系统的状态反馈鲁棒H∞控制问题和输出反馈鲁棒H∞控制问题,分别转化为辅助广义确定性离散线性系统的状态反馈H∞控制问题和输出反馈H∞控制问题。     

带丢包和量化的参数不确定系统滚动时域估计

针对网络化系统中丢包、量化和参数不确定性对状态估计的影响,提出一种带有预测补偿机制的鲁棒滚动时域估计算法。将丢包现象描述为概率已知的随机Bernoulli序列,并利用丢失数据的预测值进行丢包补偿,将数据量化引入的量化误差描述为观测方程中的一个有界不确定参数,将模型的不确定性描述为系统矩阵受到随机扰动,基于滚动优化策略,考虑量化和模型不确定性影响最严重的情况,通过滚动求解一个min-max问题得到最优状态估计器。对所提算法进行稳定性分析,推导了估计误差范数平方期望的一个上界函数,给出了估计误差范数平方期望收敛的充分条件。最后,通过仿真验证了所提算法的有效性。     

THE POLE ASSIGNMENT OF LINEAR SYSTEMS

In this paper the pole assignment problem of a time invariant linear control system issolved by using the Wu Elimination Method.In general,the questions are classified into(i)the poleassignment by using state feedback,(ii)the pole assignment by using output feedback,(iii)the poleassignment via dynamic compensator.The key point of all these problems is to solve a certaincorresponding system of polynomial equations.Based on algebraic geometry,the Wu methodprovides a mechanical algorithm for solving the system of polynomial equations.Therefore,a unifieddefinite algorithm for solving all these problems is given in this paper.During the procedure ofelimination,the unknowns are automatically separated into parameters and apparent variables.Thus,the freedom of the corresponding feedback can be defined as the number of parameters.Meanwhile,the explicit expressions of the apparent variables depending on the parameters areobtained.     

Nonlinear damped oscillators on Riemannian manifolds: Fundamentals

The classical theory of mass-spring-damper-type dynamical systems on the ordinary flat space R~3 may be generalized to higher-dimensional Riemannian manifolds by reformulating the basic underlying physical principles through differential geometry.Nonlinear dynamical systems have been studied in the scientific literature because they arise naturally from the modeling of complex physical structures and because such dynamical systems constitute the basis for several modern applications such as the secure transmission of information.The flows of nonlinear dynamical systems may evolve over time in complex,non-repeating(although deterministic) patterns.The focus of the present paper is on formulating the general equations that describe the dynamics of a point-wise particle sliding on a Riemannian manifold in a coordinate-free manner.The paper shows how the equations particularize in the case of some manifolds of interest in the scientific literature,such as the Stiefel manifold and the manifold of symmetric positive-definite matrices.