一阶耦合广义系统的极点配置问题

讨论了在工程控制中有重要意义的一阶广义分布参数系统与广义集中参数系统的耦合广义系统的极点配置问题,应用算子的广义逆给出了总理２的解及解的构造性表达式。     

一类一阶耦合广义系统的极点配置问题

讨论 Hilbert空间中广义分布参数系统与广义集中参数系统所构成的一类一阶耦合广义系统的极点配置问题 ,应用算子的广义逆给出了问题的解及解的构造性表达式。这对一阶耦合广义系统的镇定及渐近稳定性的研究具有重要的理论价值     

一种新型神经网络广义逆系统

提出一种新型带有反馈环节的广义逆系统方法,并给出了其存在性的证明．该方法首先利用神经网络构造被控对象的α 阶逆系统,通过改变反馈环节参数可随时任意配置复合系统极点,无需重新构造广义逆系统．分别对ＳＩＳＯ 和ＭＩＭＯ 非线性系统进行仿真研究．仿真结果表明,在配置极点变换时,利用该方法构造的广义逆系统仍可对原系统实现有效的线性化和解耦．     

类广义Lorenz系统的广义同步

应用广义Lorenz标准型研究了包括广义Lorenz系统、双曲型广义Lorenz系统以及Liu-Liu-Liu-Liu系统在内的类广义Lorenz系统的广义同步化问题．利用映射将一大类三阶二次混沌系统变换为广义Lorenz标准型,设计控制器使变换后的系统达到完全同步,进而使变换前的系统实现广义同步．将该方法分别用于拓扑等价和不等价的两个系统,通过数值仿真,发现结果和理论分析相符,从而表明了该方法的有效性．     

广义区间上的泛逻辑自相关系数求解

广义自相关系数的求解是泛逻辑在不确定性推理中需要解决的关键问题之一。称任意[a,b]区间为广义区间,在广义区间上给出了广义N范数、广义N性生成元、广义自相关系数的定义。提出了由复杂系统参数的分布函数求解广义自相关系数的一般方法,给出并证明了重要的直通NLK公式。最后举例说明了求解k值的具体,为从数学模型和逻辑推理两个角度来分析复杂系统参数间的相关性提供了一种新的思路。     

一类非线性系统的广义频率响应函数

基于Ｖｏｌｔｅｒａ泛函级数描述,讨论了非线性系统广义频率响应函数的概念,提出并证明了一种求解多项式类非线性系统ＧＦＲＦ的递推算法。该算法结构简单,计算量较小,优于以前的变换算法。     

在类非线性系统的广义频率响应函数

基于Ｖｏｌｔｅｒｒａ泛涵毋数描述,讨论了非线性系统广义频率响应函数的概念,提出并证明了这一种求解多项式为非线性系统ＧＦＲＦ的递推算法。该算法结构简单,计算量较小,优于以前的变换算法。     

神经网络广义逆系统控制

提出适合于高阶非线性系统线性化解耦的广义逆系统，它与被控系统复合后，不但能实现原系统的线性化和解耦，而且通过合理地设计逆系统，可使伪线性复合系统的极点在复平面上任意配置，进一步提出由静态神经网络和若干积分惯性等线性环节组成的神经网络广义逆系统，为模型未知且内部状态不易测量的高阶非线性系统的线性化解耦控制提供一条有效途径，进一步拓展了神经网络逆系统控制方法的适用范围。     

Hilbert空间中广义分布参数系统的精确能控性

首先,应用泛函分析和算子理论研究了Hilbert空间中广义算子半群的一些性质,并应用广义算子半群理论给出了Hilbert空间中广义分布参数系统的解的存在唯一性及解的构造性表达式;其次,应用泛函分析及广义算子半群理论讨论了Hilbert空间中广义分布参数系统的精确能控性。给出了精确能控的必要及充分条件。说明了广义分布参数系统精确能控性和稳定性之间的关系。所得结果对广义分布参数的研究有重要的理论意义。     

广义分布参数系统的变结构控制

研究广义分布参数系统的控制综合问题，给出了直接控制形式和分布控制形式的变结构控制设计的方法，并结合例子说明了控制的设计过程。     

不确定离散广义系统的D稳定鲁棒控制

研究了具有圆盘区域极点约束的一类不确定离散广义系统的鲁棒控制问题.首先,研 究了控制输入项不含扰动的不确定离散广义系统,提出了广义二次D镇定的概念,基于矩阵不 等式和广义Riccati方程,给出了一种广义二次D镇定器的设计方法,所得到的结论能够实现研 究目标;然后,讨论了控制输入项含有扰动的不确定离散广义系统,在一定的假设条件下,给出 了期望状态反馈增益阵的存在条件及其解析表达式.最后,用数值示例说明所给方法的有效性 及可行性.     

Solving EP singular linear systems

In this article, we deal with EP matrix and EP singular linear systems. We give some properties of EP matrix and its generalized inverse, analyze the solutions of EP systems and make some applications in Navier-Stokes equations.     

Solution of two-point-boundary-value problems by generalized orthogonal polynomials and application to optimal control of lumped and distributed parameter systems

A set of generalized orthogonal polynomials (GOPs) that can represent all types of orthogonal polynomial and non-orthogonal Taylor series are first introduced to solve dynamic state equations with two-point-boundary conditions. The basic idea is that any orthogonal polynomial function can be expressed as a power series, and vice versa. The operational matrix for the integration of the generalized orthogonal polynomials is thus derived. Using the special characteristics of these generalized orthogonal polynomials, the state equation of the two-point-boundary-value problem is thus reduced to that of an initial-value problem. This effective approach can be applied to solve the optimal control of a lumped or distributed parameter system. The computational algorithm, in conjunction with the recursive formula, is much simpler and easier than that for conventional individual orthogonal polynomials.     

Robust stability and stabilization of discrete singular systems: an equivalent characterization

This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.     

Perturbation analysis of singular linear systems with index one ∗

A new perturbation result for singular but consistent linear systems with coefficient matrix of index one is presented. However, if the system is inconsistent, we also derive a perturbation bound of the generalized linear least squares solution. Our treatment extends a classical perturbation result in numerical linear algebra.     

Exact controllability for singular distributed parameter system in Hilbert space

Exact controllability of singular distributed parameter control system is discussed via functional analysis and the theory of generalized operator semi-group in Hilbert space. Necessary and sufficient conditions concerning the exact controllability are given. Relations between exact controllability and stability of singular distributed parameter system are specified.     

基于SVD-Winograd快速变换的半盲水印算法

目前多数基于傅里叶变换域的方法,其抗几何攻击性能虽很好,嵌入的信息量也很大,但存在抗剪切攻击能力较差的问题,针对这一问题提出了一种基于奇异值分解与Winograd快速傅里叶变换相结合的半盲水印算法。在奇异值分解过程中,先将奇异值分解的对角矩阵与Winograd快速傅里叶变换中分解的对角阵进行矩阵相与,产生一新对角矩阵。再将数字水印嵌入到新对角矩阵中,最后通过相关运算提取水印。实验结果表明,该方法可获得较好的图像视觉效果,对剪切、噪声、旋转等攻击皆具有较好的鲁棒性。     

Robust input-output energy decoupling for uncertain singular systems

1 Introduction During recent years, singular systems have at- tracted the interest of a number of researchers due to the fact that they appear more naturally in the study of naturally occurring systems than regular systems (state-space systems), e.g. in economic, circuit, and boundary control systems, and chemical processes[1～3]. Many contributions have been made to the study of these systems, and a great number of results on the theory of regular systems have been generalized to the area of …     

GENERALIZED QUADRATIC STABILIZATION FOR DISCRETE‐TIME SINGULAR SYSTEMS WITH TIME‐DELAY AND NONLINEAR PERTURBATION

This paper discusses a generalized quadratic stabilization problem for a class of discrete‐time singular systems with time‐delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S‐procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete‐time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non‐singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples.