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 of linear time-invariant systems

In this paper it is shown that for any controllable linear time-invariant system, an arbitrary initial point can be driven to an arbitrary final point by means of an input, polynomial in t of degree 2k— I, with k the controllability index of the system. Also, the state trajectory is polynomial in time and of the same degree. The bound on the degree is an improvement with respect to similar results in the literature. The proof of this result is rather direct compared to the involved proof in the literature of a weaker theorem. An extension of this result considering sinusoidal inputs and state trajectories is provided.     

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.     

Controllability of generalized linear time-invariant systems

This note deals with the problem ofc-controllability of generalized systems. A new criterion for determiningc-controllability of generalized systems is established. With controllability established, it is shown that it is always possible to transfer the system from the initial position to any target by a control vector-valued function whose elements are polynomials of bounded degree. The polynomial coefficients are obtained as a solution to a set of linear equations.     

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     

Structural identifiability and observability of compartmental models of the COVID-19 pandemic

The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted their limitations. If some parameters and/or state variables of a model cannot be determined from output measurements, its ability to yield correct insights – as well as the possibility of controlling the system – may be compromised. Epidemic dynamics are commonly analysed using compartmental models, and many variations of such models have been used for analysing and predicting the evolution of the COVID-19 pandemic. In this paper we survey the different models proposed in the literature, assembling a list of 36 model structures and assessing their ability to provide reliable information. We address the problem using the control theoretic concepts of structural identifiability and observability. Since some parameters can vary during the course of an epidemic, we consider both the constant and time-varying parameter assumptions. We analyse the structural identifiability and observability of all of the models, considering all plausible choices of outputs and time-varying parameters, which leads us to analyse 255 different model versions. We classify the models according to their structural identifiability and observability under the different assumptions and discuss the implications of the results. We also illustrate with an example several alternative ways of remedying the lack of observability of a model. Our analyses provide guidelines for choosing the most informative model for each purpose, taking into account the available knowledge and measurements.     

Controllability and observability in distributed testing

In developing distributed systems, current trends are towards creating open distributed environments supporting interworking, interoperability, and portability, in spite of heterogeneity and autonomy of related systems. Several reference models, architectures and frameworks such as ODP, CORBA, and TINA, have already been designed and proposed. However, even though models, architectures, and frameworks, provide a good basis for developing working open distributed applications, conformance testing approaches are required for gaining confidence in final products and guaranteeing their integration and interoperability within open distributed environment. ODP provides some preliminary statements on conformance assessment in open distributed systems, but considerable work needs to be done before reaching a workable and accepted conformance testing methodology for open distributed processing. Further, ISO, ITU, OMG, and TINA-C, have recently recognized the urgent need for conformance testing. In this paper, we examine ideas gained from our experience with protocol testing, which may contribute to the design of such a framework. Our methodology is essentially guided by two features that have a great influence on all aspects of the testing process: controllability and observability.     

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.     

Controllability and observability of discrete models of continuous plants with higher-order holds and delay

The problem of constructing minimal state-space realizations for discrete models of continuous plants with higher-order holds and multiple delays is considered.     

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.     

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.     

Controllability,observability and duality in infinite dimensional linear systems with multiple norm-bounded controllers

Controllability of infinite-dimensional linear systems with multiple independent controllers, each of which is norm-bounded, is studied. Necessary and sufficient conditions for systems to be such are presented. Both the usual (cooperative) and the game (non-cooperative) controllability are examined. The problem of sending an initial state to some target sets is investigated. Applications to differential delay linear systems and simple distributed parameter systems are given. For the cooperative mode, a duality theory is introduced for the constrained infinite dimensional case.     

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 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, 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.     

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.