Controllability and observability of networked control systems with time-varying delays

The controllability and observability of networked control systems are studied. Aiming at the networked control system with time-varying delay, the sufficient and necessary conditions for complete controllability and complete observability of the system are presented, respectively. Because of Markov characteristic of the network-induced delay, in terms of stochastic theory, a sufficient and necessary condition for completely mean value controllability of networked control systems is obtained. Further, the conditions that the controllability and observability of networked control systems are equivalent to the initial time-invariant system are given. Controllability and observability realization indexes are also discussed, respectively. The numerical example demonstrates the effectiveness of the proposed theory.     

分数阶线性系统的能观性研究

在对一类由分数阶线性微分方程描述的系统的能观性问题研究中,通过分数阶线性定常系统求解,给出了分数阶线性定常和时变系统一般解的统一表达式。在给出分数阶系统能观性定义的基础上,提出并证明了分数阶线性系统时变和定常系统能观性的充分和必要条件,以及分数阶线性定常系统的能观性判据,所得结论对分数阶控制系统的分析与综合是有益的。     

An augmented BV setting for feedback switching control

<正> This paper considers dynamical systems under feedback with control actions limited toswitching.The authors wish to understand the closed-loop systems as approximating multi-scale problemsin which the implementation of switching merely acts on a fast scale.Such hybrid dynamicalsystems are extensively studied in the literature,but not much so far for feedback with partial stateobservation.This becomes in particular relevant when the dynamical systems are governed by partialdifferential equations.The authors introduce an augmented BV setting which permits recognition ofcertain fast scale effects and give a corresponding well-posedness result for observations with such minimalregularity.As an application for this setting,the authors show existence of solutions for systemsof semilinear hyperbolic equations under such feedback with pointwise observations.     

一类线性切换系统的能控性和能观测性的充要条件

循环不变子空间是常用于控制科学和信号处理理论的重要数学工具之一。用循环不变子空间的性质研究了切换系统的能控性和能观测性。先给出了切换系统能控性、能达性和能观测性的概念,并讨论了循环不变子空间的性质。然后用循环不变子空间的性质研究了周期线性切换系统的能控制性、能达性及能观测性,得到线性周期切换系统完全能控和完全能观测的充分必要条件。最后给出一般线性切换系统完全能控和完全能观测的充分条件和必要条件。     

Impulse observability and impulse controllability of regular degenerate evolution systems

Impulse observability and impulse controllability of regular degenerate evolution systems are discussed by using functional analysis and operator theory in Banach space. Necessary and sufficient conditions for the impulse observability and impulse controllability of the system are obtained. This research is theoretically important for studying the design of the degenerate evolution system.     

Impulse Controllability and Impulse Observability of Stochastic Singular Systems

This paper discusses the impulse controllability and impulse observability of stochastic singular systems. Firstly, the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace transform. Secondly, the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix theory. Finally, an example is given to illustrate the effectiveness of the obtained theoretical results.     

Controllability and Observability of Stochastic Singular Systems in Banach Spaces

Journal of Systems Science and Complexity - Exact (approximate) controllability and exact (approximate) observability of stochastic singular systems in Banach spaces are discussed. Firstly, the...     

OBSERVING THE HEAT EQUATION ON A TORUS ALONG A DENSE GEODESIC

Several authors have considered observability problems for the heat equation and relatedpartial differential equations.A basic problem is to determine what kinds of sampling providesufficient information to uniquely determine the initial heat distribntion.We address the case wherethe temperature is measured while travelling along a curve.We consider the special case where the space is a flat torus(of arbitrary dimension)and thecurve is a geodesic.It is shown that,in this case,the observed temperature is sufficient informationto uniquely determine the initial heat distribution if and only if the geodesic is dense in the torus.In the case of a torus,Fourier analysis techniques can be used to write down the solution of theheat equation.This allows us to derive an explicit representation of the observed temperature interms of the initial distribution.We use this representation and some ideas from the theory ofalmost periodic functions to show that the Fourier coefficients of the initial distribution can berecovered from the observation.     

Controllability of Singular Distributed Parameter Systems in the Sense of Mild Solution

Necessary and sufficient conditions for the exact controllability and approximate controllability of a singular distributed parameter system are obtained. These general results are used to examine the exact controllability and approximate controllability of the Dzektser equation in the theory of seepage.     

Application of Sturm Theorem in the Global Controllability of a Class of High Dimensional Polynomial Systems

In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress.Finally, the authors will give some examples to show the application of our results.     

Null controllability of some degenerate wave equations

This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations through a boundary controller. First, the well-posedness of linear degenerate wave equations is discussed. Then the null controllability of some degenerate wave equations is established, when a control acts on the non-degenerate boundary. Different from the known controllability results in the case that a control acts on the degenerate boundary, any initial value in state space is controllable in this case. Also, an explicit expression for the controllability time is given. Furthermore, a counterexample on the controllability is given for some other degenerate wave equations.     

挠性结构振动控制中压电致动器/敏感器的优化配置

针对挠性结构的主动振动控制问题,给出了粘贴有若干压电片的挠性梁的数学模型。基于结构模态的可控可观性,提出一种压电致动器/敏感器同位位置的优化方法。该方法利用模态在可控可观性子空间上的正交投影来反映可控可观性的测度,并根据各阶模态在系统输出中的相对重要程度加权模态可控可观测性测度,由此得到致动器/敏感器的优化配置指标。通过数学仿证明了该优化方法的有效性。     

Well-Posedness of Fully Coupled Linear Forward-Backward Stochastic Differential Equations

This paper studies the well-posedness of fully coupled linear forward-backward stochastic differential equations(FBSDEs). The authors introduce two main methods-the method of continuation under monotonicity conditions and the unified approach-to ensure the existence and uniqueness of solutions of fully coupled linear FBSDEs. The authors show that the first method(the method of continuation under monotonicity conditions) can be deduced as a special case of the second method(the unified approach). An example is given to illustrate it in linear FBSDEs case. And then, a linear transformation method in virtue of the non-degeneracy of transformation matrix is introduced for cases that the linear FBSDEs can not be dealt with by the the method of continuation under monotonicity conditions and the unified approach directly. As a powerful supplement to the the method of continuation under monotonicity conditions and the unified approach, linear transformation method overall develops the well-posedness theory of fully coupled linear forward-backward stochastic differential equations which have potential applications in optimal control and partial differential equation theory.     

GLOBAL CLASSICAL SOLUTIONS AND EXPLICITEXACT SOLUTIONS TO A KIND OF QUASILINEARPARTIAL DIFFERENTIAL EQUATIONS

1.IntroductionandMainResultTherearemanyexamplesconcerningtheformationofsingularitiesinthesoluti0nsofnon-linearpartialdifferefitialequations.Thus,althoughasolutionmaybesmoothinitially,itmaybecomesingularatsomelatertime(see[1-6]).However,T.Nishidahaspr0vedthatiftheCln0rmoftheinitialdataissufficientlysmall,thentheCauchyproblemadmitsauniqueglobalsmooths0lutionont2Otoareduciblequasilinearhyperbolicsystemwithfirst(lower)orderdissipativeterm(see[7]).Thereafter,manyauthorshavegeneralizedNishida'sr…     

项目团队的和谐能控性与和谐能观性分析

从和谐管理理论框架出发,基于项目团队系统的和谐状态模型,提出描述项目团队系统结构性质的两个概念-币口谐能控性与和谐能观性,并对其定义及适用的判别准则进行了详细的描述.分析项目团队的和谐能控性和和谐能观性,对于计算管理活动对项目团队、项目绩效的影响,优化项目团队构成具有重要的帮助,具有广泛的应用空间.     

Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps

The modelling of risky asset by stochastic processes with continuous paths, based on Brownian motions, suffers from several defects. First, the path continuity assumption does not seem reasonable in view of the possibility of sudden price variations(jumps) resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.     

单支方法的保单调性

保单调的时间离散方法求解具有非连续解的双曲型守恒律是一种常用而且有效的算法,空间离散化双曲型守恒律可得到相应的常微分方程初值问题。研究了单支方法求解上述常微分方程初值问题的非线性稳定性质,分析了单支方法的保单调性。将单支方法写为一般线性方法的形式,在步长满足一定约束条件的情况下,获得了单支方法保单调的充分条件。     

Elimination Theory in Differential and Difference Algebra

Elimination theory is central in differential and difference algebra. The Wu-Ritt characteristic set method, the resultant and the Chow form are three fundamental tools in the elimination theory for algebraic differential or difference equations. In this paper, the authors mainly present a survey of the existing work on the theory of characteristic set methods for differential and difference systems,the theory of differential Chow forms, and the theory of sparse differential and difference resultants.     

二维广义系统Roesser模型局部能达和局部能控性

研究了二维广义系统Roesser模型的性质,推导出了该系统的状态响应公式.给出了其在矩形区域上局部能达和局部能控的充分必要条件.同时,利用二维Z变换理论,给出了二维广义系统Roesser模型局部能达和局部能控的等价定义,并得出该模型相应的局部能达和局部能控的新的充分必要条件.     

Four step scheme for general Markovian forward-backward SDES

<正> This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward generator requires only mild regularity assumptions.The authors showthat the Four Step Scheme introduced by Ma,et al.(1994) is still effective in this case.Namely,the authors show that the adapted solution of the FBSDE exists and is unique over any prescribedtime duration;and the backward components can be determined explicitly by the forward componentvia the classical solution to a system of parabolic integro-partial differential equations.An importantconsequence the authors would like to draw from this fact is that,contrary to the general belief,in aMarkovian set-up the martingale representation theorem is no longer the reason for the well-posednessof the FBSDE,but rather a consequence of the existence of the solution of the decoupling integralpartialdifferential equation.Finally,the authors briefly discuss the possibility of reducing the regularityrequirements of the coefficients by using a scheme proposed by F.Delarue (2002) to the current case.