一类混杂动态系统的能控性(Ⅱ)——含单时滞的情形

首次将时滞现象引入到线性切换系统的模型中,研究含时滞的线性切换系统的能控性及其判定条件。全部工作由三部分组成。第Ⅱ部分,主要研究含单时滞的线性切换系统的能控性及其判定准则。首先给出周期型系统的单周期能控性和多周期能控性的定义和充要条件,其次给出非周期系统的能控性的定义和充要条件。     

关于周期线性系统的能控性和能稳定性

本文证明了关于周期线性系统能控性和能稳定性的两种定义的等价性,回答了Bittanti等人的一个猜想。     

一类混杂动态系统的能控性(Ⅲ)——含多时滞的情形

首次将时滞现象引入到线性切换系统的模型中,研究含有时滞线性切换系统的能控性及其判定条件。全部工作由三部分组成。第Ⅲ部分,主要研究含多时滞的线性切换系统的能控性及其判定规则。首先给出周期型系统的单周能控性和多周期能控性的定义和充要条件,其次给出非周期系统的能控性的定义和充要条件。最后,研究时滞大小不一致的情形,指出能控性与时滞大小无关。     

连续时间的IS-LM模型可控制性与仿真研究

在现代经济学的标准假设下,建立连续时间的IS-LM动态模型,分析IS-LM动态模型的系统结构特征,设计连续时间的IS-LM动态模型的控制律,得到控制律的解析解并进行仿真分析。研究表明：连续时间的IS-LM动态模型具有能控性、能达性和完全能观性等系统结构特征;连续时间IS-LM动态模型系统可以任意配置其极点,使模型系统渐进稳定,达到输出调节并具有满意的动态性能,即在现代经济学的标准假设下,证实了IS-LM动态模型的可控性。根据模型假设及模型参数的经济意义设计仿真实验,仿真实验结果验证了所设计反馈控制律对连续时间IS-LM动态模型控制的有效性。因而,针对复杂多变的经济形势,科学设计经济政策,能有效实现经济调控的目标。     

离散事件动态系统的能达能观性与对干扰解耦的周期合并配置

能达与不能达子空间,能观与不能观子空间是 Wonham 教授创建的多变量控制几何方法的几个基本概念.对 DEDS 文献[2,3]提出了分别能达概念及其充要条件;文[2]还给出了与能达有关的标准结构;文[3]提出了上界能观及其充要条件;文[4]给出了用反馈合并周期的充分条件;文[5]得到了用输出反馈合并配置周期的充要条件.在以上文献     

存在趋势和周期特征的非平稳时间序列的建模及其应用

本文研究存在未知周期和趋势的非平稳时间序列的估计问题.将经典的时间序列分解模型写成一个含有未知参数的部分线性模型,首先采用B-样条逼近未知时间趋势,然后利用惩罚最小二乘回归法得到未知周期、周期序列和趋势的估计.本文还给出估计量的理论性质,包括周期估计的相合性以及周期序列和趋势估计的渐近性质.模拟研究展现了本文方法的优越...     

带扩散项人口模型的能稳性

该文研究了一类带扩散项的人口模型平衡解的反馈能稳性,控制器由对应于平衡解的线性化系统的LQ问题所导出.     

周期Stokes方程源的识别问题(英文)

本文研究了周期Stokes方程中源的识别问题.利用能观性不等式,得到了识别问题解的存在性,同时给出了该问题的逼近过程.     

一类具有变消耗率的恒化器模型的脉冲扰动与分支

提出和研究了一个具有变消耗率和非同步脉冲的恒化器模型,并且得到了一组像阈值一样的条件来确保系统半平凡周期解的全局渐稳性,系统的持久性以及出现非平凡分支周期解,最后,一些数值模拟体现了该模型的动力学性态.     

极小-极大-加系统的周期时间的输出反馈独立配置

在数字电路中, 两个时间信号通过逻辑电路的与门相当于极大运算, 通过逻辑电路的或门相当于极小运算. 极小—极大—加系统可用于数字电路的时间分析. 对于一类非线性极小—极大—加系统(F, G, H), 运用极大—加代数和有向图方法得到了在输出反馈作用下的周期时间能独立配置的一个充分条件.     

Vibrational stabilization and the Brockett problem

The present paper deals with the exposition of methods for solving the Brockett problem on the stabilization of linear control systems by a nonstationary feedback. The paper consists of two parts. We consider continuous linear control systems in the first part and discrete systems in the second part. In the first part, we consider two approaches to the solution of the Brockett problem. The first approach permits one to obtain low-frequency stabilization, and the second part deals with high-frequency stabilization. Both approaches permit one to derive necessary and sufficient stabilization conditions for two-dimensional (and three-dimensional, for the first approach) linear systems with scalar inputs and outputs. In the second part, we consider an analog of the Brockett problem for discrete linear control systems. Sufficient conditions for low-frequency stabilization of linear discrete systems are obtained with the use of a piecewise constant periodic feedback with sufficiently large period. We obtain necessary and sufficient conditions for the stabilization of two-dimensional discrete systems. In the second part, we also consider the control problem for the spectrum (the pole assignment problem) of the monodromy matrix for discrete systems with a periodic feedback.     

Event-triggered control for sampled-data set stabilization of switched delayed boolean control networks

This paper considers the event-triggered control design for the uniform sampled-data set stabilization of switched delayed Boolean control networks (SDBCNs). First, using the algebraic state space representation method, SDBCNs are converted into the equivalent algebraic form. Second, using the algebraic form, the uniform sampled-data reachable sets are constructed, based on which, a necessary and sufficient condition is obtained for the uniform sampled-data set stabilization of SDBCNs. Finally, the event-triggered mechanism is presented, and a sufficient condition is proposed to design the time-variant state feedback event-triggered controller for the uniform sampled-data set stabilization of SDBCNs.     

Stabilization and set stabilization of switched Boolean control networks via flipping mechanism

Stabilization and set stabilization of switched Boolean control networks are investigated by using flipping mechanism in this paper. Firstly, with the help of Warshall algorithm, an explicit criterion for the stabilization of switched Boolean control networks is derived. Secondly, the necessary and sufficient condition for the solvability of stabilization of switched Boolean control networks, by flipping some elements of perturbation set once, is presented. Thirdly, a search algorithm is proposed to calculate the minimum number of stabilization flipped nodes and what exactly they are. Furthermore, a necessary and sufficient condition is established for the solvability of set stabilization of switched Boolean control networks by flipping some elements of perturbation set once. Analogously, an algorithm is given to find the minimum number of set stabilization flipped nodes. Finally, examples are shown to demonstrate the feasibility of the above results.     

广义时变系统的鲁棒容错控制

针对广义时变系统的鲁棒容错控制问题,基于矩阵不等式及建立Lyapunov方程的方法,首先,在系统出现执行器故障的情况下,分别给出了两种广义时变系统模型鲁棒镇定的充要条件.接着,在系统出现外部干扰的情况下,给出了相应模型鲁棒镇定的充分条件,同时给出了相应的容错控制器的设计方法.     

一组系统的同时稳定化

本文利用Youla参数化方法研究了多于3个系统的一组线性时变系统的同时稳定化问题,给出了这样系统稳定的一个充要条件.     

H∞强镇定问题的新解法

H∞强镇定问题可解的原始算法是依赖于一个解存在的充分条件．自然的此算法应用起来有一定的局限性．针对此问题，首先给出H∞强镇定问题可解的一个充要条件．并说明该条件在计算上很容易实现的．并由此充要条件出发设计了一个简单且实际可行的算法．该算法实际上没有局限性，而且比较利于计算机编程．最后举例说明新算法与H∞强镇定问题可解的原有算法相比，具有更大的优点．     

时变系统的稳定化

This paper deals with the stabilization problem for linear time-varying systems within the framework of nest algebras. We give a necessary and sufficient condition for a class of plants to be stabilizable, and we also study the simultaneous and strong stabilization problems.     

Simultaneous stabilization of linear plants by a low order controller

We consider simultaneous stabilization of linear scalar stationary plants of second order and derive an easily verified necessary condition of simultaneous stabilization, as well as a sufficient condition that leads to a constructive algorithm for a stabilizing controller. The existence of a stabilizing controller is established in the parametric polynomial space by a method that finds the stability radii of polynomials.     

一类非线性系统的局部镇定

研究一类非线性系统的局部状态反馈镇定问题．基于中心流形理论,给出一类非线性系统渐近镇定的充分条件,并设计出镇定系统的反馈控制律．文中利用具有齐次导数的Lyapunov函数方法,特别研究了一类平面非线性系统及具有二重零特征值的一类非线性系统的渐近镇定问题,给出了系统镇定的若干充分条件,并构造出控制律．文中的例表明了所得结果的有效性．     

分派问题保持最优解不变的充分必要条件

进一步讨论了在保持分派问题最优解不变的情况下,效率矩阵元素的变化范围.这些变化范围是保持分派问题最优解不变的充要条件.