带扩散项单种群模型的精确能控性

本文研究了一类单种群生态模型的精确能控性问题.利用线性化系统的Carleman估计和Kakutani不动点定理,证明了该模型稳态解的局部能控性.它反应了外部控制在种群演变过程中的影响作用.     

非线性中立型控制系统函数能控性

本文讨论形如的非线性中立型控制系统函数能控性．给出该类系统的函数能控性和零函数能控性的判定定理．所得结果在实际系统的设计、分析等方面是非常实用的．     

Banach空间中无限维线性系统的能控性

研究在非自反状态空间和自反控制空间中无限维线性系统x(t)=Ax(t) Bu(t)的精确能控性和精确零能控性.当A生成C-半群时,得到这个系统关于Lp([O,T],U),1＜p≤∞精确能控和精确零能控的等价判据.当A生成CO-半群时,也得到系统关于Lp([O,T],U),1＜p≤∞的精确零能控的充要条件.这些结论是对经典控制理论的有益发展和补充,还给出所得抽象结论的两个应用.     

Banach空间中无限维线性系统的能控性

研究在非自反状态空间和自反控制空间中无限维线性系统x(t)=Ax(t) Bu(t)的精确能控性和精确零能控性.当A生成C-半群时,得到这个系统关于L~p([O,T],U),1相似文献   

滞后控制系统的完全能控性、毕竟能控性、最终能控性和拟能控性

讨论时滞控制系统的能控性 .指出与无时滞系统不同的是 ,该类系统的能控性与终点时刻有一定的关系 .由此给出一系列与终点时刻有关的能控性 ,即完全能控性、毕竟能控性、最终能控性等 ,并得到一些判定定理 .     

一类非线性chemotaxis系统的局部零能控性

本文研究了一类非线性chemotaxis系统的能控性问题.利用这类线性化结合不动点的方法,获得了非线性系统的局部零能控性结果,推广了非线性抛物-椭圆型方程能控性的结果.     

分布参数系统能控能观性问题的统一处理及应用

本文的主要目的是介绍一个统一的处理分布参数系统能控能观性问题的方法,并给出该方法在分布参数控制理论中的应用。为此,本文将从一类“类抛物” 偏微分算子（即没有椭圆性条件）的带权恒等式出发,给出所有已知的关于抛物型方程、双曲型方程、Schrödinger 方程和板方程的基于整体Carleman 估计的能控能观性结果。同时,基于该带权的恒等式,本文还给出它在双曲型系统的稳定性问题和在拟线性复Ginzburg-Landau 方程能控能观性等问题中的应用。     

椭圆-抛物系统的近似能控性

设计了两类控制器同时作用于椭圆-抛物系统:一类是传统的内部控制(分布控制器);另一类是以一个时变系数形式描述的内部控制(块控制器,κ(t)只是和时间有关,而与空间位置x没有关系,所以称块控制器,是相对于分布控制而言的).由于这里讨论的系统是非线性的,也只能得到全局近似能控性,不能得到精确零能控性.设计这样的控制器的目的...     

边值系统的能控性与能观测性问题

把抽象系统的能控性和能观测性推广到由强连续双半群描述的抽象边值系统,给出了相应的边值系统能控性的充要条件,并研究了能观测性与能控性之间的对偶关系.最后作为例子,研究了双曲系统能控性.文中所得的结果可用于讨论现代物理系统中出现一类边值系统的能控性与能观测性问题.     

由退化抛物方程支配串联系统的零能控性

该文讨论了由一个半线性退化抛物方程与半线性热方程构成的串联系统的零能控性. 这里控制函数仅施加在一个方程上. 证明的关键是建立适当的能观性不等式.     

OPTIMAL CONTROL PROBLEM FOR PARABOLIC VARIATIONAL INEQUALITIES

1 IntroductionThroughout this paPer, we denote n an opell bounded domain in Rn with smooth boulldary0fl, let Q = fl x (0,T) and r = 0n x (0,T). Let H = L'(n).We shall study the optimal control problems governed by the following system:y'(t) Ay(t) p(y(t) -- rk(t)) 9 B1u(t) I1(t), (1.1)y(0) = u0,rk'(t) Aop(f) 7(op(f)) = B2u(t) f2(f), (1.2)op(0) = op0with the state constrchtF(y) C W' (1.3)The pay-off functional is given byJ(y, u) = l"[,(,, y) h(u)]dt. (1.4)JoNote that y' and…     

Time optimal boundary controls for the heat equation

The fact that the time optimal controls for parabolic equations have the bang–bang property has been recently proved for controls distributed inside the considered domain (interior control). The main result in this article asserts that the boundary controls for the heat equation have the same property, at least in rectangular domains. This result is proved by combining methods from traditionally distinct fields: the Lebeau–Robbiano strategy for null controllability and estimates of the controllability cost in small time for parabolic systems, on one side, and a Remez-type inequality for Müntz spaces and a generalization of Turán?s inequality, on the other side.     

Remarks on exact controllability for Stokes and Navier–Stokes systems

This Note deals with the controllability of Stokes and Navier–Stokes systems with distributed controls with support in possibly small subdomains. We first present a new global Carleman inequality for the solutions to Stokes-like systems that leads to the null controllability at any time T>0. Then, we present a local result concerning exact controllability to trajectories of the Navier–Stokes system. To cite this article: E. Fernández-Cara et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Estimate on the Pathwise Lyapunov Exponent of Linear Stochastic Differential Equations with Constant Coefficients

In this article, we study the problem of estimating the pathwise Lyapunov exponent for linear stochastic systems with multiplicative noise and constant coefficients. We present a Lyapunov type matrix inequality that is closely related to this problem, and show under what conditions we can solve the matrix inequality. From this we can deduce an upper bound for the Lyapunov exponent. In the converse direction, it is shown that a necessary condition for the stochastic system to be pathwise asymptotically stable can be formulated in terms of controllability properties of the matrices involved.     

Controllability of nonlinear systems

Some sufficient conditions are presented for the controllability of general nonlinear systems. First, the controllability problem is transformed into the problem of existence of fixed points for some operator; using Schauder's theorem, it is derived that a sufficient condition for controllability is the existence of a subsetS inC _n+m (T) which is invariant for a derived operator. Secondly, with the aid of the notion of comparison principle, the existence of the subsetS is guaranteed by the existence of solutions for some nonlinear integral inequality or equality equations. For example, one solution for such nonlinear integral equations is obtained under the assumption of the uniform boundedness for a nonlinear term of the differential equation.     

Simultaneous controllability of damped wave equations

We study the exact controllability of q uncoupled damped string equations by means of the same control function. This property is called simultaneous controllability. An observability inequality is proved, which implies the simultaneous controllability of the system. Our results generalize the previous results on the linear wave without the dampings. Copyright © 2016 John Wiley & Sons, Ltd.     

Exact controllability of a fluid–rigid body system

This paper is devoted to the controllability of a 2D fluid–structure system. The fluid is viscous and incompressible and its motion is modelled by the Navier–Stokes equations whereas the structure is a rigid ball which satisfies Newton's laws. We prove the local null controllability for the velocities of the fluid and of the rigid body and the exact controllability for the position of the rigid body. An important part of the proof relies on a new Carleman inequality for an auxiliary linear system coupling the Stokes equations with some ordinary differential equations.     

Controllability and quadratic stability quadratic stabilization of discrete-time interval systems--an LMI approach

^** Email: qlzhang{at}mail.neu.edu.cn This paper presents necessary and sufficient conditions fordiscrete-time interval systems to be quadratically stable orquadratically stabilizable, and sufficient conditions for discrete-timeinterval systems to be controllable. All the results are obtainedin terms of linear matrix inequality (LMI). With the LMI toolbox,the problems can be conveniently solved. Illustrative numericalexamples show that the results are effective and less conservativeto check the robust controllability and stability and to designthe stabilizing controller for discrete-time interval systems.     

Local exact controllability of the Navier–Stokes system

In this paper we deal with the local exact controllability of the Navier–Stokes system with distributed controls supported in small sets. In a first step, we present a new Carleman inequality for the linearized Navier–Stokes system, which leads to null controllability at any time T>0. Then, we deduce a local result concerning the exact controllability to the trajectories of the Navier–Stokes system.