广义区间系统可控和可观测的充分条件

分别给出了单输入多输出广义区间系统可控和多输入单输出广义区间系统可观测的充分条件     

Generalized Gram Matrix and Its Application to the Observability Problem for Linear Nonsteady Systems

Sufficient conditions for the nondegeneracy of a generalized Gram matrix are obtained. In particular, it is shown that the generalized Gram matrix is nondegenerate for the Chebyshev systems of functions. An application of the results to the observability problems for linear nonsteady systems of ordinary differential equations are given. In terms of the observability matrix, necessary and sufficient conditions of the complete and total observability by means of finite-parameter solving operations are established.     

Exact Boundary Controllability and Exact Boundary Observability for a Coupled System of Quasilinear Wave Equations

Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local boundary(weak) observability for a coupled system of 1-D quasilinear wave equations with various types of boundary conditions.     

Boundary Controllability and Observability of a One-Dimensional Nonuniform SCOLE System

A hybrid system, composed of an elastic beam governed by an Euler-Bernoulli beam equation with variable coefficients and a linked rigid body governed by an ordinary differential equation, is considered. Various controllability/observability properties of the system under bounday control/observation are studied. It is shown that an open-loop smooth/singular controller of either torque control or force control is sufficient to make the system exactly controllable in arbitrarily short time duration. The work was carried out with the support of the National Natural Science Foundation of China and the Russian Foundation for Fundamental Researches, Grant 02-01-00554.     

An Example on the Controllability of Perturbed Linear Control Systems

We show by an example that small perturbations with respect to the convergence in measure of the coefficients A and B may affect the complete controllability of the linear control system , where x is the state and u is the control. This answers a question raised in Ref. 1.     

Exact Controllability of Semilinear Evolution Systems and Its Application

In this paper, we obtain several abstract results concerning the exact controllability of semilinear evolution systems. First, we prove the null local exact controllability of semilinear first-order systems by means of the contraction mapping principle; in this case, we do not assume any compactness. Next, we derive the global and/or local exact controllability of semilinear second-order systems by means of the Schauder fixed-point theorem; in this case, we assume only the embedding of the related spaces having some compactness, which is reasonable for many concrete problems. Our main result shows that the observability of the dual of the linearized system implies the exact controllability of the original semilinear system. Finally, we apply our abstract results to the exact controllability of the semilinear wave equation.     

线性脉冲控制系统的能控性与最优控制

首先讨论了一类线性随机脉冲控制系统的精确能控性质,给出了该类控制系统的脉冲精确能控的等价的代数判据.然后提出了一个确定性的二维线性脉冲控制系统的时间-脉冲强度最优控制问题;利用动态规划原理,给出了脉冲最优控制的反馈形式和值函数的显式表达式;说明了值函数在整个平面上是连续的,在左右两个半平面的内部还是连续可微的.     

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L~p([O,T],U),1相似文献   

线性定常系统规范结构分解问题的研究

单输入单输出线性定常系统的状态空间按能控性和能观测性进行结构分解,能全面、完整的反映系统的各个子系统特性,理论上揭示状态空间的本质特征.通过规范性分解,不完全能控和不完全能观测的连续时间线性时不变系统可分解为"能控能观测","能控不能观测","不能控能观测","不能控不能观测"四个子空间,但是其分解后子空间的维度受非奇异变换矩阵P_c的影响.提出了一种约束变量的方法,用来选取P_c中列向量的规则,以控制原系统分解后子空间的表现形式.经实例验算,方法简单有效,具有一定的教学和理论意义.     

Controllability and observability of impulsive hybrid dynamic systems

Corresponding author, Email: cbsoh{at}auto.eee.ntu.ac.sg This paper considers the controllability and observability ofhybrid dynamic systems with impulsive switching of the otherwisecontinuously evolving state. It derives necessary and sufficientconditions for impulsive hybrid dynamic systems to be controllableand observable.     

A Survey of Reachability and Controllability for Positive Linear Systems

This paper is a survey of reachability and controllability results for discrete-time positive linear systems. It presents a variety of criteria in both algebraic and digraph forms for recognising these fundamental system properties with direct implications not only in dynamic optimization problems (such as those arising in inventory and production control, manpower planning, scheduling and other areas of operations research) but also in studying properties of reachable sets, in feedback control problems, and others. The paper highlights the intrinsic combinatorial structure of reachable/controllable positive linear systems and reveals the monomial components of such systems. The system matrix decomposition into monomial components is demonstrated by solving some illustrative examples.     

一维线性波动方程耦合组的精确边界同步能观性

作者介绍了多种精确同步能观性,并对一维波动方程耦合组在多种边界条件下分别实现了精确边界同步能观性,分组精确边界同步能观性以及分组精确边界零能观性与同步能观性.     

Controllability properties of constrained linear systems

In this paper, we present results on constrained controllability for linear control systems. The controls are constrained to take values in a compact set containing the origin. We use the results on reachability properties discussed in Ref. 1.We prove that controllability of an arbitrary pointp inR ⁿ is equivalent to an inclusion property of the reachable sets at certain positive times. We also develop geometric properties ofG, the set of all nonnegative times at whichp is controllable, and ofC, the set of all controllable points. We characterize the setC for the given system and provide additional spectrum-dependent structure.We show that, for the given linear system, several notions of constrained controllability of the pointp are the same, and thus the setC is open. We also provide a necessary condition for small-time (differential or local) constrained controllability ofp.This work was supported in part by NSF Grant ECS-86-09586.     

仿射系统局部强可控性的充分条件

本文讨论仿射系统的局部强可控性.文中证明了如果系统在x_0点满足可控性秩条件,并且集合{x|dim sp{g_i(x)}相似文献   

双曲系统的节点状态的精确边界能控性

在此综述性文章中,我们将回顾关于节点状态的精确边界能控性的已有结果,并对此主题之进一步研究给出若干建议     

Controllability of Nonlinear Systems in Banach Spaces: A Survey

This paper presents a survey on research using fixed-point theorems and semigroup theory to study the controllability of nonlinear systems and functional integrodifferential systems in Banach spaces. Also discussed is the use of this technique in K-controllability and boundary controllability problems for nonlinear systems and integrodifferential systems in abstract spaces.     

一类具独立子系统的退化时滞控制系统的能控性

讨论退化时滞微分控制系统的能控性问题.首先将退化时滞微分控制系统化为标准形式,除去关联项,得到具独立子系统的退化时滞微分控制系统.然后就一般的退化时滞微分控制系统,得到其能控的充要条件为其可达集等于全空间.对于具独立子系统的广义时滞控制系统,给出其能控的充要条件为每个子系统的可达集等于其相应的子空间,并给出其能控的代数判据,最后举例说明主要结果的应用.     

Exact Controllability for a Class of Nonlinear Evolution Control Systems

In this paper, we study the exact controllability of the nonlinear control systems. The controllability results by using the monotone operator theory are es-tablished. No compactness assumptions are im...     

Null Controllability in Unbounded Domains for the Semilinear Heat Equation with Nonlinearities Involving Gradient Terms

We consider the null controllability problem for the semilinear heat equation with nonlinearities involving gradient terms in an unbounded domain of ^N with Dirichlet boundary conditions. The control is assumed to be distributed along a subdomain such that the uncontrolled region \ is bounded. Using Carleman inequalities, we prove first the null controllability of the linearized equation. Then, by a fixed-point method, we obtain the main result for the semilinear case. This result asserts that, when the nonlinearity is ^C1 and globally Lipschitz, the system is null controllable.