广义系统能控性的几个注记

本文首先给出了广义系统能控性与正常系统能控性的关系,并由此讨论了广义系统最优 经济结构综合问题及能控性程度的度量形式.最后给出了工程算例.     

能控广义系统与不能控广义系统集之间的距离

本文讨论了能控广义系统与不能控广义系统集之间的距离问题,得出了该距离的下界估 计式及相应的算法.     

能控（观）广义系统集的拓扑结构*

本文讨论了能控(观)广义系统集的开性和稠密性,并从能控(观)正则系统集的拓扑结构出发,讨论了相应的广义系统集的连通性,得到了较好的结果,从而将有关正则系统的结果推广到了广义系统。     

广义系统的能控、能观性判别条件

该文讨论广义系统能控、能观性问题,给出了广义系统能控和能观性一种新的判别条件.     

矩阵束A＋BKC的最小秩及其应用

给出矩阵束Ａ＋ＢＫＣ当Ｋ变化时的最小秩表示公式，并讨论了最小秩在广义系统的特征结构配置与动态阶配置方面的应用。     

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。     

广义动态系统的微分算子矩阵方法

本文用微分算子矩阵方法讨论了一类广义动态系统的结构性质,并且用微分算子多项式 矩阵的系数阵,给出了各类动态系统能控(观)性的直接判据.它是用微分算子矩阵方法研究 广义动态系统的开端.     

线性时变广义系统的能控性与能观性问题

讨论了线性时变系统和线性时变广义系统的两个基本问题, 得到了两种判定时变系统能控性与能观性的必要条件, 该判定条件只依赖于系统矩阵A(t)和输入矩阵B(t), 不必计算系统的系统状态转移矩阵, 使得判别时变系统能控性与能观性易于实现. 说明了本文结论是线性定常系统相应结论的自然扩展. 对进一步深入研究时变系统和时变广义系统具有实际启发作用.     

时变广义系统线性二次最优控制

研究时变广义系统线性二次最优控制问题.通过引进时变广义系统脉冲能控性及脉冲能 观性等概念,建立了这类问题与标准状态空间系统二次指标问题的等价性.进而证明了解的 存在唯一性,给出了解的表示和最优反馈综合.     

广义线性系统的结构分类方法

基于受限等价变换的结构分析方法,提出实现多个矩阵的同时标准化的方法,从而得到广义系统的标准型,该方法使复杂的广义系统等价于多种简单的系统;根据标准型的特点,对分解后的多种简单广义系统进行细化分类;对不同类型的简单广义系统的控制方法进行研究,使复杂广义系统的控制问题转化为简单广义系统的控制问题。数值仿真结果表明,该方法对广义系统的结构的分类更细致具体,便于后续对广义系统的解、脉冲及其能控等方面进行更深入的研究,理论创新前景十分广阔。     

Optimal singular control for nonlinear semistabilisation

The singular optimal control problem for asymptotic stabilisation has been extensively studied in the literature. In this paper, the optimal singular control problem is extended to address a weaker version of closed-loop stability, namely, semistability, which is of paramount importance for consensus control of network dynamical systems. Three approaches are presented to address the nonlinear semistable singular control problem. Namely, a singular perturbation method is presented to construct a state-feedback singular controller that guarantees closed-loop semistability for nonlinear systems. In this approach, we show that for a non-negative cost-to-go function the minimum cost of a nonlinear semistabilising singular controller is lower than the minimum cost of a singular controller that guarantees asymptotic stability of the closed-loop system. In the second approach, we solve the nonlinear semistable singular control problem by using the cost-to-go function to cancel the singularities in the corresponding Hamilton–Jacobi–Bellman equation. For this case, we show that the minimum value of the singular performance measure is zero. Finally, we provide a framework based on the concepts of state-feedback linearisation and feedback equivalence to solve the singular control problem for semistabilisation of nonlinear dynamical systems. For this approach, we also show that the minimum value of the singular performance measure is zero. Three numerical examples are presented to demonstrate the efficacy of the proposed singular semistabilisation frameworks.     

Lipschitz广义非线性系统观测器设计

研究一类广义非线性系统的观测器设计问题．首先讨论了半正定Lyapunov函数下指数1广义非线性系统稳定及渐近稳定性,然后对一类由线性和Lipschitz非线性项组成的广义非线性系统,给出了渐近稳定观测器存在的条件,并把观测器反馈增益矩阵的设计归结为广义线性系统容许控制以及奇异值计算问题,证明了若容许广义线性系统矩阵的最小奇异值大于系统的Lipschitz常数,容许控制器增益矩阵就是待求的观测器反馈增益矩阵。     

多输入多输出线性定常系统稳定裕度的分析与改进

针对多输入多输出(MIMO)控制系统的稳定裕度求解问题,首先分析了现有的回差阵奇异值法这一计算方法,并得到其解决单输入单输出(SISO)系统的稳定裕度结论,在此基础上,提出两种基于系统回差阵的稳定裕度改进方法;一种是在有限条件下利用矩阵的特征值代替奇异值来建立与稳定裕度关系的策略,另一种是利用系统逆回差阵的行列式,通过求其奇异值来计算系统稳定裕度;最后结合工程实例,通过数值仿真验证两种稳定裕度计算方法相比原方法都有不同程度的改进,而且三种方法可以结合起来进行分析,最大化的减小系统稳定裕度结果的保守性.     

Stability margins of singular perturbation systems via state-feedback control

The gain and phase margins of singular perturbation systems are analysed under unmodelled high-frequency dynamics control, composite control, and the original full-order linear quadratic (LQ) control. The analysis is on the basis that there is a good relation between the minimum singular value of return difference transfer matrix and the stability margins. We begin with the examination of stability margins of subsystems and then show that state-feedback control design of subsystems could preserve gain and phase margins for the original full-order singularly perturbed system if the singular perturbation parameter epsiv; is sufficiently small. The effectiveness of ε on stability margins is formulated and determined. It is found that the effectiveness can be evaluated by a simple method. Two examples are exploited to illustrate the analytic results.     

离散广义大系统的Lyapunov稳定性分析

广义大系统的稳定性是广义大系统理论的基本问题之一,对其稳定性的研究要比状态空间大系统复杂得多,因为广义大系统不仅需要考虑稳定性,而且还要考虑正则性和因果性(离散广义系统)及脉冲自由(连续广义系统).本文在所有孤立子系统都是正则的且具有因果关系的条件下,利用Lyapunov方程,应用Lyapunov函数方法,研究了广义离散线性大系统和广义离散非线性大系统的稳定性和不稳定性问题,给出了离散广义大系统稳定性和不稳定性判定定理,得到了离散广义大系统的关联稳定参数域和不稳定域.     

非线性广义系统的变结构控制设计

从线性定常广义系统出发，研究非线性广义系统的变结构控制设计问题。其主要思想为：选取一具有指定性能的线性定常广义系统作为参考模型，根据所控系统与参考模型的误差方程设计变结构控制，使系统的状态（输出）向参考模型的状态（输出）逼近，由参考模型的性能即得所研究的非线性广义系统所希望的性能。仿真例子验证了所建立方法的有效性。     

The single-input Minimal Controllability Problem for structured systems

This paper considers the Minimal Controllability Problem (MCP), i.e. the problem of controlling a linear system with an input vector having as few non-zero entries as possible. We focus on structured systems which represent an interesting class of parameter dependent linear systems and look for structural controllability properties based on the sparsity pattern of the input vector. We show first that the MCP is solvable when a rank condition is satisfied and show that generically one non-zero entry in the input vector is sufficient to achieve controllability when there is no specific system structure. According to the fixed zero/non-zero pattern of the state matrix entries, we give an explicit characterization of the minimum number and the possible location of non-zero entries in the input vector to ensure generic controllability. The analysis based on graph tools provides with a simple polynomial MCP solution and highlights the structural mechanisms that make it useful to act on some variables to ensure controllability.     

General response formula and minimum energy control for the generalsingular model of 2-D systems

The general response formula for the general singular model of 2-D linear systems is derived. The concepts of local reachability and local controllability are extended to the singular model. Necessary and sufficient conditions for local reachability and local controllability are established. The minimum energy control problem for the singular model is formulated and solved     

基于聚类和SVD算法的模糊逻辑系统结构辨识

为了研究模糊逻辑系统新的结构辨识方法, 提出采用基于山峰函数的减法聚类算法构造模糊逻辑系统的初始结构, 并利用奇异值分解(SVD)算法分析了模糊规则与奇异值、累积贡献率以及索引向量的关系, 从而实现了模糊逻辑结构的优化. 最后, 对该算法的可行性和有效性进行了仿真验证和性能比较, 取得了较好的效果.