布尔控制网络的能控性与能观性

利用矩阵的半张量积,布尔控制网络被转化为离散时间系统.本文从离散时间系统的结构矩阵出发,讨论了逻辑控制系统的能控能观性条件,得到了一个新的能控性条件.新的条件简化了原有能控性矩阵的计算复杂性,矩阵的最高阶数由原来的2m+n降到了2n.另外,还得到了检验布尔控制网络能观性的条件.与原有条件相比,新的条件更容易计算检验.最后,给出一个实例,检验给出的能控能观性判断条件的正确性.     

网络控制系统的能控性和能观性

给出了网络控制系统的定义，并基于线性时不变系统的被控对象，建立了传感器为时钟驱动，控制器和作动器为事件驱动时长时滞网络控制系统的数学模型，对网络控制系统的均值能控、均方能控、均值能观及均方能观作了定义，得到了网络控制系统能控的充分或必要条件及能观的充要条件．     

Controllability and observability of switched multi-agent systems

This paper considers controllability and observability of switched multi-agent systems, which are composed of continuous-time and discrete-time subsystems. First, a controllability criterion is established in terms of the system matrices. Then, by virtue of the concepts of the invariant subspace and the controllable state set, a method is proposed to construct the switching sequence to ensure controllability of switched multi-agent systems, and a necessary and sufficient condition is obtained for controllability. Moreover, a necessary controllability condition is derived in terms of eigenvectors of the Laplican matrix. With respect to observability, two necessary and sufficient algebraic conditions are obtained. Finally, simulation examples are provided to illustrate the theoretical results.     

Controllability and observability of Boolean control networks

The controllability and observability of Boolean control networks are investigated. After a brief review on converting a logic dynamics to a discrete-time linear dynamics with a transition matrix, some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix. Based on the discrete-time dynamics, the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely. Then the problem of observability is also solved by giving necessary and sufficient conditions.     

Controllability, observability, and duality in singular systems

The concepts of controllability and observability for systems of the formEdot{x} = Ax + Bu, y = Cx, Esingular are considered. A theory is presented which unifies the three main approaches to this topic already existing in the literature. The development includes a generalization of the duality theorem from state-space theory.     

Controllability and observability of linear time-invariant compartmental models

The problems of complete controllability and complete observability of linear time-invariant compartmental models with general input-output structures are considered. The analysis of these problems is based largely on graph-theoretic methods and the properties of polynomial matrices. Specifically, statements on complete controllability and complete observability are proven by using graphical constructions which do not change the basic properties of controllability and observability. The major results of this paper are: 1) A unique decomposition of the digraph of a compartmental model into sources, sinks, and transits. 2) A theorem which states that a compartmental model with closed sinks is completely observable if and only if the matrix [C^{T}, A^{T}] is full rank, and a corollary which provides a sufficient condition for complete observability of all other linear time-invariant compartmental models. 3) A theorem which states that a single sink compartmental model is completely controllable if and only if a compartment from each source is controlled. 4) A controllability algorithm which provides sets of excitations which are sufficient for complete controllability of any linear time-invariant compartmental model.     

Controllability and observability for affine nonlinear Hamiltonian systems

It is shown that an affine nonlinear Hamiltonian system is "controllable" if and only if it is "observable," in the sense that strong accessibility implies local weak observability and vice versa. Furthermore, it is shown that a nonminimal Hamiltonian system can be reduced to a locally weakly observable and strongly accessible system, in such a way that the reduced system is again Hamiltonian.     

Controllability and observability of linear time varying singularsystems

Controllability and observability of analytically solvable linear time varying singular systems are considered. Our analysis includes the possible impulsive zero-input response. Based on the definitions of controllability and observability naturally extended from the ones adopted in the time-invariant setting, sufficient and necessary conditions for these two properties are derived. Furthermore, according to the specific definitions of these concepts used here, the authors show that the dual relationship between controllability and observability does not hold     

Controllability and observability of periodic hybrid interval systems

This paper derives necessary and sufficient conditions for periodic hybrid interval systems where the A, B and C system matrices are interval matrices to be controllable and observable. The results are easily extended to impulsive periodic hybrid interval systems and linear discrete-time systems.     

Controllability and observability criteria for multivariable linear second-order models

Criteria are discussed for the determination of controllability, stabilizability, observability, or detectability of linear second-order multivariable models of, for example, large space structures. An initial modal transformation is not required and the criteria are thus applicable to models with arbitrary damping coefficients. Moreover, the criteria are modal in the sense that some or all of the modes may be tested for controllability, or observability. This aspect has advantages if not all the modes are known or easily computable. The criteria are further illustrated for a number of important special cases in a series of corollaries.     

Controllability and observability at infinity of multivariable linear second-order models

In this note we give, in the spirit of [4], numerically attractive tests of controllability and observability of linear multivariable second-order systems in which the leading matrix is singular.     

Comments on "Controllability and observability of composite systems"

In a recent paper, a sufficient condition for controllability (observability) of two systems connected in tandem having the most general Jordan form of representation was given. In this correspondence, a counterexample to this sufficient condition is given and further assumptions under which this condition is necessary as well as sufficient are indicated.     

Discrete-time observability for distributed parameter systems

The aim of this paper is to study the observability for systems described by first-order evolution equations and for those described by second-order evolution equations in the case of discrete-time observations. For the systems with a finite number of sensors we present necessary and sufficient conditions for observability. We show that these distributed parameter systems are never finite-step observable. We give the restricted sets of the initial-state spaces whose elements are N-step observable. We also investigate the relations between the systems with discrete-time observations and the systems with continuous-time observations from the viewpoint of observability Moreover, we see the essential difference between the parabolic case and the hyperbolic case.     

Controllability and observability of multi-agent systems with heterogeneous and switching topologies

ABSTRACT

This paper focuses on controllability and observability of multi-agent systems with heterogeneous and switching topologies, where the first- and the second-order information interaction topologies are different and switching. First, based on the controllable state set, a controllability criterion is obtained in terms of the controllability matrix corresponding to the switching sequence. Next, by virtue of the subspace sequence, two necessary and sufficient algebraic conditions are established for controllability in terms of the system matrices corresponding to all the possible topologies. Furthermore, controllability is considered from the graphic perspective. It is proved that the system is controllable if the union graph of all the possible topologies is controllable. With respect to observability, two sufficient and necessary conditions are derived by taking advantage of the system matrices and the corresponding invariant subspace, respectively. Finally, some simulation examples are worked out to illustrate the theoretical results.     

Regional observability for distributed semi-linear hyperbolic systems

The objective of this paper is to study the notion of regional observability of hyperbolic semilinear systems. For the state reconstruction in a given subregion, we give a first approach which combines the extension of the HUM method and the fixed point techniques. The analytical case is then explored using sectorial property of the considered dynamic operator and converted to a fixed point problem. The two approaches lead to algorithms which are successfully implemented numerically and illustrated with examples and simulations.     

Controllability and observability for time‐varying switched impulsive controlled systems

This paper is concerned with the controllability and observability for linear time‐varying switched impulsive systems. First, some new results about the variation of parameters for time‐varying switched impulsive systems are derived. Then less conservative sufficient conditions and necessary conditions for state controllability and observability of such systems are established. And for such system without impulsive control input, sufficient and necessary conditions for controllability and observability are derived. Furthermore, corresponding criteria applied to time‐varying impulsive systems are also discussed and examples are presented to show the effectiveness of the proposed results. Copyright © 2009 John Wiley & Sons, Ltd.     

Principal component analysis in linear systems: Controllability, observability, and model reduction

Kalman's minimal realization theory involves geometric objects (controllable, unobservable subspaces) which are subject to structural instability. Specifically, arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces. This situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization. Structural instability associated with geometric theories is not unique to control; it arises in the theory of linear equations as well. In this setting, the computational problems have been studied for decades and excellent tools have been developed for coping with the situation. One of the main goals of this paper is to call attention to principal component analysis (Hotelling, 1933), and an algorithm (Golub and Reinsch, 1970) for computing the singular value decompositon of a matrix. Together they form a powerful tool for coping with structural instability in dynamic systems. As developed in this paper, principal component analysis is a technique for analyzing signals. (Singular value decomposition provides the computational machinery.) For this reason, Kalman's minimal realization theory is recast in terms of responses to injected signals. Application of the signal analysis to controllability and observability leads to a coordinate system in which the "internally balanced" model has special properties. For asymptotically stable systems, this yields working approximations ofX_{c}, X_{bar{o}}, the controllable and unobservable subspaces. It is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces.