双线性系统可控性综述

双线性系统是一类特殊的非线性系统,广泛存在于现实世界中,如工程、经济、生物、生态等领域,被认为是最接近于线性系统的非线性系统．对双线性系统的研究已历经了近半个世纪. 作为系统最基本的属性,双线性系统可控性的研究一直以来是热点和难点.本文分别对连续双线性系统可控性和离散双线性系统可控性进行讨论, 综述了双线性系统可控性的研究.特别地,报告了近来对离散双线性系统可控性研究的新成果.最后,例举了一些可控的双线性系统例子.     

微分代数系统的实时控制计算

文中提出微分代数系统的一些实时控制计算方法，进行误差估计，给出了采样间隔与控制误差的关系。对于一个模型问题进行了稳定性分析，画出稳定区域，给出保证控制稳定的采样间隔的取值范围。     

线性中立型多时滞系统李代数稳定性判据

研究了线性中立型多时滞微分系统的稳定性。从矩阵李代数可解性角度,推导出新的简单的时滞独立稳定性判据。该新判据的重要意义和优越性在于首次突破了以往相关文献的稳定性判据在应用上受条件mΣj=1‖Cj‖<1或ρ(mΣj=1︱Cj︱)<1的限制,从而首次成功确定了在mΣj=1‖Cj‖≥1和ρ(mΣj=1︱Cj︱)≥1的情形下中立型多时滞微分系统的渐近稳定性。最后,通过两个例子显示了新判据的优越性。     

基于李代数的变形目标跟踪

动态几何变形是图像跟踪技术面临的突出难题之一. 本文提出基于李代数的变形目标跟踪方法, 用Gabor特征表征目标, 以仿射李群建立目标几何变形, 利用李代数和李群之间的指数映射将参数的最优化求解从欧氏空间转至光滑流形, 实现了对变形目标的稳定跟踪.从物理层面分析了目标跟踪过程中的参数几何变换的实质, 从理论上对在光滑流形上进行迭代求解的优点进行了详细分析, 并对其收敛性做出了证明.图像序列跟踪测试的对比实验表明, 本文方法较现有基于欧氏空间的算法在收敛速度、跟踪稳定性和精确性方面有显著提高.     

基于量子逻辑的下推自动机的代数刻画

首先,本文提出量子下推自动机（简记为L-VPDA）的概念,从代数角度出发详细研究了此类自动机的性质,同时建立此类自动机的代数刻画,即利用量子状态构造证明了任意L-VPDA与状态转移为经典函数且具有量子终状态的L-VPDA间的相互等价性;其次详细研究了量子上下文无关语言的代数刻画以及对于正则运算的封闭性。     

微分代数系统的数值仿真算法

介绍了微分代数系统ＤＡＥ的基本概念及仿真算法,特别指出了用ＢＤＦ方法求解高指标常系数线性ＤＡＥ系统时的数值稳定性缺陷。最后,针对飞行器轨道约束实时控制问题,给出了３阶收敛的代数约束算法。     

基于李雅普诺夫量子系统控制方法的状态调控

从多方面对基于李雅普诺夫的量子系统控制方法进行了系统深入地研究, 包括该方法与最优控制的关系; 李雅普诺夫函数与性能指标之间的关系; 几种常用李雅普诺夫函数下的控制所能解决的问题, 适用范围和所存在的问题等. 在此基础上, 结合量子系统本身所具有的特点, 分别针对本征态, 叠加态和混合态的制备与调控目标, 总结出多种不同控制问题的改进方案. 对不同改进方案的设计思想, 所能解决的问题, 物理意义及其适用范围等进行剖析, 系统化了一套基于李雅普诺夫稳定性理论对量子系统进行状态调控的设计方法.     

基于光量子芯片的量子自旋链中完美态转移可编程量子模拟

近些年,量子计算物理实现技术进步很快,构建能够发挥实际用途的量子计算装置成为发展重点。采用量子模拟研究量子自旋系统的演化行为,相比于经典模拟会更加高效。一维量子自旋链中完美态转移模型在量子通信和量子计算领域具有重要的研究价值。提出一种基于双光子连续时间量子漫步的可编程完美态转移量子模拟方法,并且基于光量子芯片完成了2类特殊哈密顿量作用下XY型量子自旋链中双激发“周期-镜像”完美态转移的量子模拟实验,为模拟量子自旋系统的演化提供了一种实用且可扩展的实验方案。     

离散事件动态系统的代数模型及其控制器的分析计算

本文在离散事件动态系统的Ｐｅｔｒｉ网图形描述的基础上建立了相应的代数模型，该模型可以用来计算无竞争无回路Ｐｅｔｒｉ网的“最大状态”；该“最大状态”的计算在本文给出的动态反馈控制器中得到了应用。     

Homomorphisms and controllability of parallel composite systems

The concept of a homorphism is introduced to study the local weak controllability of parallel composite analytic systems. If two systems are simultaneously homomorphic to a nontrivial system, then their parallel composition is not locally weakly controllable. The converse, however, is not true. It is this negative aspect that shows the complexity of nonlinear systems in contrast with the linear ones.     

On the controllability of nonlinear systems with symmetry

Sufficient and necessary conditions are given for the controllability of nonlinear systems possesing symmetry.     

Local controllability for families of diffeomorphisms

We study groups and semigroups which are generated by analytic families of diffeomorphisms. The central notion is that of local controllability of a family of diffeomorphisms at a given point of the state manifold, which generalizes the familiar notion of local controllability of control systems with continuous, as well as discrete time. Lie theory methods are used. We systematically exploit the so called fast switching variations and properties of the jet spaces of curves on the state manifold.     

Motion planning for control-affine systems satisfying low-order controllability conditions

This paper is devoted to the motion planning problem for control-affine systems by using trigonometric polynomials as control functions. The class of systems under consideration satisfies the controllability rank condition with the Lie brackets up to the second order. The approach proposed here allows to reduce a point-to-point control problem to solving a system of algebraic equations. The local solvability of that system is proved, and formulas for the parameters of control functions are presented. Our local and global control design schemes are illustrated by several examples.     

Commutative algebraic methods for controllability of discrete-time polynomial systems

In this paper, we consider controllability of discrete-time polynomial systems. First, we present a forward accessibility (local reachability) condition that can be verified in finite time, in contrast to conventional conditions. Second, we give a backward accessibility (local controllability) condition for an invertible system and a condition to verify invertibility. Finally, we derive sufficient conditions to test whether the forward accessible system is reachable and to test the backward accessible system is controllable.     

Local controllability of nonlinear systems

The local controllability of control systems with an arbitrary number of controls is considered, first on an open set and then at a given point; necessary conditions are derived concerning the Lie algebra T′ generated by the input vector fields, and applied to gradient systems.The main results are a geometric sufficient condition for local controllability at a point, and an equivalent condition based on the computation of Lie brackets, assuming T′ to be (n − 1)-dimensional.     

Partial controllability of stochastic linear systems

The controllability concepts for linear stochastic differential equations, driven by different kinds of noise processes, can be reduced to the partial controllability concepts for the same systems, driven by correlated white noises. Based on this fact, in this article, we study the conditions of exact and approximate controllability for linear stochastic control systems under various kinds of noise processes, including correlated white noises as well as coloured, wide band and shifted white noises. It is proved that such systems are never exactly controllable while their approximate controllability is equivalent to the approximate controllability of the associated linear deterministic systems at all past time moments.     

多智能体网络系统的能控性代数条件

能控性是多智能体系统研究的核心问题,主要包括结构可控性和精准可控性。对多智能体系统的模型和能控性代数条件进行了总结。在相对协议和绝对协议条件下,运用图论和矩阵论的知识系统分析了多智能体系统能控性的代数条件。按照同质多智能体到异质多智能体的顺序,对现有的多智能体系统模型和代数条件进行了梳理,并在已有结论的基础上对多智能体系统能控性的代数条件进行了改善,进一步提出了新的代数条件。多智能体能控性代数条件的改进大大简化了能控性的计算量。     

Local controllability of non-linear systems: An example

An example of a locally controllable nonlinear system on R³ is given. The system is of the type with f, g analytic vector fields and u bounded. The fields f and g are such that the dimension of the vector space spanned at x₀ by the Lie brackets which contain g an odd number of times is 2.     

多智能体系统可控性的图论刻画

研究领航者-跟随者结构多智能体系统的可控性问题.利用松弛的等价分化刻画了系统可控性与信息拓扑结构之间的关系,为系统可控性提供了基于图论的判别方法.基于置换群理论将对称的概念推广到多领航者系统,并证明了3种图论工具（对称性、等价分化和松弛的等价分化）之间的包含关系.仿真结果验证了所提出方法的有效性.