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。     

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.     

Recent progress on controllability/observability for systems governed by partial differential equations

<正> The main purpose of this paper is to overview some recent methods and results on controllability/observability problems for systems governed by partial differential equations.First,the authorsreview the theory for linear partial differential equations,including the iteration method for the nullcontrollability of the time-invariant heat equation and the Rellich-type multiplier method for the exactcontrollability of the time-invariant wave equation,and especially a unified controllability/observabilitytheory for parabolic and hyperbolic equations based on a global Carleman estimate.Then,the authorspresent sharp global controllability results for both semi-linear parabolic and hyperbolic equations,based on linearization approach,sharp observability estimates for the corresponding linearized systemsand the fixed point argument.Finally,the authors survey the local null controllability resultfor a class of quasilinear parabolic equations based on the global Carleman estimate,and the localexact controllability result for general hyperbolic equations based on a new unbounded perturbationtechnique.     

On nearly-controllable subspaces of a class of discrete-time bilinear systems

If a linear time-invariant system is uncontrollable, then the state space can be decomposed as a direct sum of a controllable subspace and an uncontrollable subspace. In this paper, for a class of discrete-time bilinear systems which are uncontrollable but can be nearly controllable, by studying the nearly-controllable subspaces and defining the near-controllability index, the controllability properties of the systems are fully characterized. Examples are provided to illustrate the conceptions and results of the paper.     

On controllability for stochastic control systems when the coefficient is time-variant

<正> This paper investigates the controllability problem of time-variant linear stochastic controlsystems.A sufficient and necessary condition is established for stochastic exact controllability,whichprovides a useful algebraic criterion for stochastic control systems.Furthermore,when the stochasticsystems degenerate to deterministic systems,the algebraic criterion becomes the counterpart for thecomplete controllability of deterministic control systems.     

关于一类线性时不变切换系统的脉冲控制

针对一类线性时不变脉冲切换系统,利用Lyapunov函数导出了一种有效的控制方法.首先,建立了这类系统在任意切换率下稳定与渐近稳定的充分条件;然后,给出了这类系统在设定的切换率下指数稳定的判别准则;最后,给出了一个数值例子及仿真来阐明结论的正确性.     

Controllability of General Linear Discrete Multi-Agent Systems with Directed and Weighted Signed Network

This paper investigates the controllability of general linear discrete-time multi-agent systems with directed and weighted signed networks by using graphic and algebraic methods. The non-delay and delay cases are considered respectively. For the case of no time delay, the upper bound condition of the controllable subspace is given by using the equitable partition method, and the influence of coefficient matrix selection of individual dynamics is illustrated. For the case of single delay and multiple delays, the equitable partition method is extended to deal with time-delay systems, and some conclusions are obtained. In particular, some simplified algebraic criteria for controllability of systems with time delay are obtained by using augmented system method and traditional algebraic controllability criteria.

     

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。     

On the Solutions of the Matrix Equations in Optimal Stochastic Control

1.INTRoDUCTIoNoFTHEPRoBLEMConsiderthetime-invariantlinearIt6stochasticsystemwherexER,uCRm,FER""",BER""m,a=const.(i=1,2,'',k)arenaturalnumbers;W(t)=[W(t),W2(t),Wk(t)]"(tSo)isak-dimensionalstandardWienerprocesswithindependentcomponentsdefinedonthecompleteprobabilityspace(fl,FP),(A,B)iscontrollable.SupposethatRERm"m,QERmxmaregivenpositivedefiniteweightingmatrices,Ereferstothemathematicalexpectation.ConsidertheoptimalstochasticcontrolDroblemItiswell-knownthatifthereisapositive…     

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.     

具有异步时延的网络化控制系统故障检测

针对具有异步信号时延的离散系统，研究了在异步时延下基于观测器的故障检测及其设计问题。首先提出了一个存在异步时延下系统的故障检测模型，该模型保持了系统的定常性和时不主特性。同时在此模型上构造了异步时延系统的状态观测器，并依据系统观测误差通过合理地选择湮灭加权矩阵的方法构建了频域内的故障检测残差发生器。最后通过一个摆式列车试验模型的仿真检验了设计方法的有效性。     

Moment Equations of Linear It Stochastic Systems with Applications

1.INTRODUCTIONAsiswellknown,stochasticsystemmodeloftheIt6typeisoneofthemostimportantmodelsforstochasticsystems,manystochasticsystemswithcolorednoisecanbestudiedwithhelpoftheIt6stochasticsystems[if.ForthestabilityandcontrolproblemofIt6stochasticsystems,nlallyresultshavebeenobtainedintheliteratures[l~6].Whilesomebasicproblems,suchasthenecessaryandsufficientconditionofmean-squarestabilityoflinearIt6stochasticsystems,havehotbeensolved.Inthepreviousliterature,someresultsonthestabilityoflinear…     

网络控制系统的可镇定性和可检测性

基于线性时不变系统的被控对象，建立了控制器为事件驱动时长时延网络控制系统的数学模型，对网络控制系统的均值可镇定性、均方可镇定性、均值可检测性和均方可检测性作了定义，得到了网络控制系统可镇定、可检测的充要条件，最后以不稳定的倒立摆为对象进行了仿真研究．     

Robust Finite-Time Stability and Stabilization of a Class of Fractional-Order Switched Nonlinear Systems

This paper deals with the problem of finite-time boundedness and finite-time stabilization boundedness of fractional-order switched nonlinear systems with exogenous inputs. By constructing a simple Lyapunov-like function and using some properties of Caputo derivative, the authors obtain some new sufficient conditions for the problem via linear matrix inequalities, which can be efficiently solved by using existing convex algorithms. A constructive geometric is used to design switching laws amongst the subsystems. The obtained results are more general and useful than some existing works, and cover them as special cases, in which only linear fractional-order systems were presented. Numerical examples are provided to demonstrate the effectiveness of the proposed results.     

基于非线性观测器实现一类分数阶混沌系统的同步

分数阶混沌系统的同步控制是近年来研究的热点,本文研究了一类分数阶混沌系统的同步控制问题.对满足存在一个特定的状态变量作为系统输出条件的单输出分数阶混沌系统,依据分数阶混沌系统的非线性观测器理论和稳定性理论,讨论了其非线性观测器的设计问题.对该类分数阶混沌系统,给出了一个合适的控制器S,在此控制输入下仅利用系统的一个状态变量xi及其对时间的分数阶导数x(α)i、x(2α)i就可以使观测器的状态变量与被观测分数阶系统的状态变量达到同步.理论分析及仿真结果都证明了该同步方案的有效性.     

Positive-Controllability,Positive-Near-Controllability,and Canonical Forms of Driftless Discrete-Time Bilinear Systems

Controllable canonical forms play important roles in the analysis and design of control systems. In this paper, a fundamental class of discrete-time bilinear systems are considered. Such systems are of interest since, on one hand, they have the most complete controllability theory. On the other hand, they can be nearly-controllable even if controllability fails. Firstly, controllability of the systems with positive control inputs is studied and necessary and sufficient algebraic criteria for positive-controllability and positive-near-controllability are derived. Then, controllable canonical forms and nearly-controllable canonical forms of the systems are presented, respectively, where the corresponding transformation matrices are also explicitly constructed. Examples are given to demonstrate the effectiveness of the derived controllability criteria and controllable canonical forms.

     

DISTURBANCE ATTENUATION VIA STATE-FEEDBACK CONTROLLERS

1.IntroductionandPreliminaryKnowledgeAcommonproblemmetinthedesignofacontrolsystemistheexternaldisturbancesuchaswhitenoiseorotherkindofunwelcomevariables.Thus,weneedsomedesignmethodstoreducetheeffectofdisturbancetoanacceptablelevel.WeknowthatHOOoptindzationisanefficienttechniquetodothisjob,andmanypapershaveappearedonthistopic,see[1,2].momthesepapers,weknowthatiftheplatstatesareavailableforfeedbaCk,andthereisnodirecttransmissionfromthedisturbanceandcolltrolinputtothecolltrolledoutput,thentheno…     

块对角可控规范型多输入线性系统及极点配置

基于向量空间的模结构分解和矩阵的有理标准形给出了定常多输入线性系统一类新的块对角可控规范型,其中的系统矩阵相似与一个块对角矩阵,该块对角矩阵类似于矩阵的有理标准形,与现在有的可控规范型比较,更容易反映系统的结构特征,证明步骤给出了求解方法。作为一个应用,讨论了定常多输入线性系统的极点配置问题,得到了反馈增益矩阵的一般表达式,此表达式中含有任意参数,此方法将多输入线性系统极点配置问题转化为个数为系统矩阵循环指数的单输入系统的极点配置问题,进而推导出确定一个反馈增益矩阵的最少元素个数即为系统的阶数。     

新分段分数阶混沌系统的同步控制

通过改变修正的Lorenz-Stenflo (modified Lorenz-Stenflo, MLS)混沌系统的分段函数项,得到了一个新的四维分段混沌系统。新系统较MLS混沌系统具有更低的分数阶维数,在3.44阶时仍具有混沌特性。根据分数阶系统的线性稳定性理论和非线性反馈控制方法,提出了新分数阶系统的状态同步方法。通过理论推导,得到了两个混沌系统的同步稳定条件。控制器能够自适应地根据误差大小调节反馈系数,缩短同步时间。最后对3.6阶的分数阶系统进行了同步仿真实验,仿真结果验证了改进算法能够加快同步速度。     

OUTPUT VARIABLE STRUCTURE CONTROL FOR TIME-INVARIANT LINEAR TIME-DELAY SINGULAR SYSTEM

Synthesis and design of output variable structure controller for time-invariant linear timedelay singular system are studied. In the case that the system is regular and the system index is one, switching function with integral compensator and variable structure controller are designed, which guarantee that the sliding mode is asymptotically stable and the solution trajectory of the system arrives at the switching manifold in limited time. The design method is applicable to the systems which can be regularized. Finally, a numerical example is given to demonstrate effectiveness and simplicity of the design method.