一类广义不确定线性系统稳定控制

本文讨论一类广义不确定线性系统Ex’(t)=(A+δA)x(t)+(B+δB)u(t)的稳定控制问题,这里，E为奇异阵；δA∈UA(α) δB∈UB(β)均为系统的不稳定量，UA(α)、UB(β)为某类集合，α>0, 0<β<（√2-1）。在广义线性系统Ex’(t)=Ax(t)+Bu(t)能稳、能正常化条件下，上述不确定系统具有稳定鲁棒控制器，并且该控制器可消除该系统的脉冲行为。     

对偶关系与不确定系统的状态估计

本文讨论如下系统状态估计问题, x=A(t)x+B1(t)u(t)+B2(t)w y=C(t)X+D1(t)u(t)+D2(t)w 其中u(t)为已知输入向量,w为不确定向量.假定w为时间t 的函数,对它只知道其可能的变化范围,不知道其具体实现.问题是根据量测y(t),0tT,如何去估计状态变量 x(T)?我们用[1]中所建立的对偶关系式解决了状态的min-max估计问题.在二次型限制之下的min-max状态估计与卡尔曼滤波完全一致.这里所用的方法比起[4]中的方法简单得多.     

泛逻辑泛运算模型之间的关系*

研究泛逻辑的泛与运算模型、泛或运算模型与模糊非之间的关系。证明了零级泛与运算模型T(x,y,h)、零级泛或运算模型S(x, y, h)与强非N(x)=1-x形成De Morgan三元组,当h∈(0, 0.75), 零级泛或运算S(x, y, h)=(min(xm+ym, 1))1/m, N(x)=(1-xm)1/m时, T, S, N形成一个强De Morgan三元组。进一步证明了一级泛与运算模型T(x, y, h, k)、一级泛或运算模型S(x, y, h, k)与N(x)=(1-xn)1/n满足De Morgan定律;特别当h∈(0, 075), 一级泛或运算模型S(x, y, h, k)=(min(xnm+ynm, 1))1/nm, N(x)=(1-xnm)1/nm时, T, S, N形成一个强De Morgan三元组。     

对倪茂林、张汉国同志所提问题[1]的答复

1.设计自适应律的维数问题在文[2]中,设x(t)∈R~n,y(t)∈R~m,u(t)的维数为p(p≤n),设计的自适应律为△A=K_1(x~T(t)+u~T(t))ε(t), (3.1) △B=K_2(x~T(t)+u~T(t))ε(t)。 (3.2) 这一过程用到了增补(3.1),(3.2)式中各项的维数的分析方法。比如:u(t)∈R~p,设为u(t)=(u_1(t),u_2(t),…,u_p(t)),那么在与状态向量x~T(t)相加时,将u~T(t)的P维扩成n维,只在后面补零即可。 u~T(t)=(u_1(t),u_2(t),…,u_p(t),0…0)~T。这一过程的意义是把P维的输入向量假想成n维输入,n-p个输入实际上是不存在的,令这n-p个输入全为零,这对分析问题是很有好处的,这样的处理在实际问题中也是常用的。     

套代数上的(m,n)-导子

设m和n是任意固定的非零整数且(m+n)(m-n)≠0,AlgΝ是一个套代数,δ是AlgΝ上的一个自映射。证明了如果对任意的算子A,B∈A lgΝ有mδ(AB)+nδ(BA)=mδ(A)B+m Aδ(B)+nδ(B)A+n Bδ(A),则δ是一个导子。     

混合H_2/H_∞控制问题的降阶控制器

1　引言考虑 np 广义被控对象z0z1y=P(δ) wu =AC0C1C2　 B1 　 B2D0 1 　 0D1 1 　 D1 2D2 1 　 0　　　　wu ,(1)其中 A BC D :=C(δI- A) - 1 B D,δ在连续和离散情形分别表示拉氏变换算子 s,Z-变换算子 z,x∈ Rnp,y∈ Rny,w∈ Rnw,u∈ Rnu分别为广义对象、量测、外部输入和控制变量 .z0∈Rnz0 ,z1 ∈ Rnz1 分别为与 H2 ,H∞ 指标相关的控制输出信号 .所谓混合 H2 / H∞ 控制是指 :设计控制器 K ,使得 Tz0 w 2 极小 ,且 Tz1 w∞ <1.其中 Tziw(δ)是从 w到 zi 的闭环传传递函数 (i=0 ,1) .其意义在于可使系统在具有稳定性…     

第八届世界自控联(IFAC)大会论文评介(二)

近年来,对扩散型的非线性随机微分方程 dx(t)=f(x(t))dt+g(x(t))dw(t) dy(t)=h(x(t))dt+dv(t),较多的工作集中在研究给定{y(s),o≤s≤t}后x(t)的条件密度v_t(dx)上,形成当前非线性滤波研究中的重要方向。     

On the stabilization of switched linear stochastic systems with unobservable switching laws

1 Introduction Consider the following switched linear stochastic system dx(t) = Aθtx(t)dt +Bθtu(t)dt + Fθtdwt, E x0 2 < ∞ (1) where x0 = x(0). The system state x(t) ∈ Rn is completely observable and u(t) ∈ Rr is the input. The system noise {wt} is an l-dimensional standard Wiener process, which is independent of {x(s),s t}. Aθt, Bθt, Fθt are coefficient matrices with suitable dimensions. The switching law (or signal) θt : [0, ∞) → Θ is a piecewise constant function of time. I…     

一类控制有约束的非线性系统的全局可控性

本文考虑非线性控制系统x=A(t)x+K(t,u)+g(t,x,u),u∈Ω(t)的全局可控性,去掉了文献[2,3,4]中关于X~(-1)(t)g(t,x,u)(X(t)是微分方程x=A(t)x的标准基解矩阵)积分有界的要求,得到了充分条件,并举例说明其应用。     

具有状态和控制滞后不确定系统的保性能控制器设计

1　引言本文的目的在于将文献 [1 ]的结论推广到同时具有状态和控制滞后的不确定系统 ,并进而研究其最优保性能控制问题 .考虑具有状态和控制滞后的不确定系统x( t) =[A DF( t) E1 ] x( t) [Ad DF( t) Ed] x( t-d) [B DF( t) E2 ] u( t) [Bh DF( t) Eh]《u》( t-     

广义分散控制系统的脉冲固定模

本文讨论了广义分散控制系统的脉冲固定模问题,给出了广义分散控制系统没有脉冲固定模的几何与代数判据,并得到了广义分散系统能分散正常化的一个充要条件。     

Leader-following Consensus of Multi-agent Systems via a Hybrid Protocol with Saturation Effects

In this paper, a hybrid protocol which can control multi-agent systems to achieve “leader-following consensus” is proposed, the control protocol is periodic and is composed of continuous control and impulse control. Considering the power limitation and the time error of the actual industrial production equipments, the impulse saturation effects and the impulse time window are introduced. In this paper, the multi-agent system is modeled, one of the agents is designated as the leader, and the rest of the agents are the followers. Then the error system equations of the multi-agent system is derived. The stability of the error system is analyzed by constructing the Lyapunov function. Theorem 1 and theorem 2 are obtained as the criteria of state consensus of the multi-agent system. Finally, a numerical experiment is carried out to verify the reliability and efficiency of the conclusions are given in this paper. Because it takes into account the impulse time window and impulse saturation effects, which is more in line with the actual industrial production.

     

不确定广义系统的鲁棒脉冲耗散控制

本文在状态空间下, 基于线性矩阵不等式(LMI)的方法, 研究了一类不确定广义系统在允许的不确定性下的脉冲耗散控制问题, 并且通过解线性矩阵不等式得到了此类不确定广义系统对于允许的不确定性的鲁棒脉冲耗散状态反馈控制器和输出反馈控制器, 最后通过数值算例验证了定理的可行性.     

广义时变脉冲系统的时域稳定

研究了状态依赖广义时变脉冲系统的时域稳定问题.基于微分矩阵不等式 (Differential matrix inequalities, DMI) 和S-procedure理论, 给出了两类状态依赖广义时变脉冲系统时域稳定的充分条件.接下来, 根据给出的充分条件设计了状态反馈控制器, 使得闭环系统时域稳定.最后, 给出数值算例来验证结论的有效性.     

Stability of Takagi–Sugeno Fuzzy Delay Systems With Impulse

The Takagi-Sugeno (T-S) model of fuzzy delay systems with impulse is first presented in this paper. By means of classical analysis methods and Razumikhin technique, the criteria of uniform stability and uniform asymptotic stability for T-S fuzzy delay systems with impulse are obtained, respectively. Three numerical examples are also discussed to illustrate the efficiency of the obtained results.     

Impulse Analysis of Linear Time-Varying Singular Systems

Impulsive part of solution to initial value problem of linear time-varying singular systems is given explicitly. Impulse observability and impulse controllability for the systems are redefined     

带有脉冲模的广义控制系统设计

本文对带有脉冲模的广义控制系统给出了一种输入输出可逆变换标准结构分解。利用这种标准结构分解,使得广义控制系统设计变得非常直观和简单,易于工程实现。     

不确定切换奇异时滞系统鲁棒指数容许性分析

讨论一类连续时间不确定切换奇异区间时变时滞系统的鲁棒指数容许性问题. 通过定义衰减率依赖李亚普诺夫函数并利用平均驻留时间法, 给出一个时滞区间依赖充分条件保证标称系统正则、无脉冲且均方指数稳定. 同时该准则也被推广至不确定系统. 本文获得的结论为连续时间切换奇异时滞系统的基本问题提供了一个解, 即识别切换信号使得切换奇异时滞系统正则、无脉冲且均方指数稳定. 数值例子说明本文结果的有效性.     

A Constructive Approach to Approximate Linear Periodic Systems

In this note, the problem on approximating a linear periodic system with period N by a periodic model with period M(0infin norms. Under this framework, both finite impulse response (FIR) and infinite impulse response (IIR) periodic systems can be efficiently approximated by using a constructive linear matrix inequality approach. Finally, some numerical examples are given to illustrate the effectiveness of the proposed approach     

Equalization of Multichannel Acoustic Systems in Oversampled Subbands

Equalization of room transfer functions (RTFs) is an important topic with several applications in acoustic signal processing. RTFs are often modeled as finite-impulse response filters, characterized by orders of thousands of taps and non-minimum phase. In practice, only approximate estimates of the actual RTFs are available due to measurement noise, limited estimation accuracy, and temporal variation of source–receiver position. These issues make equalization a difficult problem. In this paper, we discuss multichannel equalization with focus on inexact RTF estimates. We present a multichannel method for the equalization filter design utilizing decimated and oversampled subbands, where the full-band acoustic impulse response is decomposed into equivalent subband filters prior to equalization. This technique is not only more computationally efficient but also more robust to impulse response inaccuracies compared with the full-band counterpart.