Partial state and input observability recovering by additional sensor implementation: a graph–theoretic approach

This article deals with the problem of additional sensor location in order to recover the observability of any given part of the state and unknown input for structured linear systems. The proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system's structure. We first provide graphical and necessary sufficient conditions for the generic observability of any given part of the state and input. Then, we study the number and location of additional sensors in order to satisfy the latter conditions. On the one hand, we provide necessary requirements to be satisfied by these additional sensors. On the other hand, we give other sufficient simple conditions allowing us to add a number, which is guaranteed to be minimal, of sensors to ensure the observability of any given part of the state and unknown input.     

State and input observability recovering by additional sensor implementation: A graph-theoretic approach

This paper deals with the problem of additional sensor location in order to recover the state and input observability for structured linear systems. The proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system’s structure. It allows one to provide the minimal number of the required sensors and either their pertinent location or a necessary and sufficient condition which allows one to check if a sensor location is adequate or not. We obtain a sensor placement procedure based on classical and well-known graph theory algorithms, which have polynomial complexity orders.     

Partial state observability recovering for linear systems by additional sensor implementation

This paper deals with the problem of additional sensor location in order to recover the observability of any given part of the state for structured linear systems. The proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system’s structure. We first provide new graphical necessary and sufficient conditions for the generic partial observability. Then, we study the location of additional sensors in order to satisfy the latter conditions. We provide necessary and sufficient requirements to be satisfied by these additional sensors and all their possible locations. The proposed solution is simple to implement because it is based on well-known algorithms, usually used for finding successors and predecessors of vertex subsets or on computation of maximal linkings in a digraph. All the used algorithms have polynomial complexity orders.     

State and input observability for structured linear systems: A graph-theoretic approach

This paper deals with the state and input observability analysis for structured linear systems with unknown inputs. The proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system's structure. Using a particular decomposition of the systems into two subsystems, we express, in simple graphic terms, necessary and sufficient conditions for the generic state and input observability. These conditions are easy to check because they are based on comparison of integers and on finding particular subgraphs in a digraph. Therefore, our approach is suited to study large-scale systems.     

Controllability and observability of 2D thermal flow in bulk storage facilities using sensitivity fields

To control and observe spatially distributed thermal flow systems, the controllable field and observable field around the actuator and sensor are of interest, respectively. For spatially distributed systems, the classical systems theoretical concepts of controllability and observability are, in general, difficult to apply. In this study, sensitivity fields were used to analyse the behaviour from input to state and from initial state to output. For the analysis of controllability and observability, a large-scale, bulk storage facility with coupled thermal flow of air and agro-products was used. Analysis of this system using the classical systems theory results in controllability and observability results that are dependent on the step size of the spatially discretised system. Due to matrix multiplications, inaccurate results are calculated if the step size is too small. Our findings indicate that input-state and initial-state output sensitivity fields provide sufficient information about the controllability and observability of large coupled spatially distributed systems, using finite-dimensional state space representation with small discretisation steps.     

Sensor location for discrete mode observability of switching linear systems with unknown inputs

This paper deals with the problem of additional sensor placement in order to recover the discrete mode observability of switching structured linear systems with unknown inputs. Such a property is quite important for designing control laws, observers, fault detection and isolation schemes (when the fault occurrence implies a commutation between two modes), and so on. The proposed method, based on a graph-theoretic approach, assumes only the knowledge of the system’s structure. We express, in graphical terms, new necessary and sufficient conditions for discrete mode generic observability. When these conditions are not satisfied, we propose a sensor placement procedure which allows us to recover the mode observability. Our approach can be implemented by classical and quite simple graph-theory algorithms.     

Observability of switching structured linear systems with unknown input. A graph-theoretic approach

This paper deals with the observability of the discrete mode, the internal state and the input of switching structured linear systems with unknown input. The proposed method, based on a graph-theoretic approach, assumes only the knowledge of the system’s structure. We express, in graphical terms, necessary and sufficient conditions for the generic observability of the discrete mode, the continuous internal state and the input of a switching structured linear system. These conditions can be implemented by classical graph theory algorithms based on finding particular paths and cycles in a digraph.     

Observability for bilinear systems

Since the observability for bilinear systems is affected by the input, this paper defines three kinds of observability for bilinear systems ; namely (1) observability with some input, (2) observability with any input, (3) observability with unknown input. The necessary and sufficient condition for the observability with some input and sufficient conditions for the observability with any input and with unknown input for discrete bilinear systems are derived respectively and the effects of the input are clarified     

Generic uniform observability analysis for bilinear systems

In this paper, we study the property of generic uniform observability for structured bilinear systems. More precisely, to check whether or not a structured bilinear system is generically uniformly observable, we provide a group of necessary conditions and a second group of sufficient ones. These conditions are expressed in quite simple graphic-terms. On one hand, all the given conditions are easy to check because they deal with finding paths in a digraph. On the other hand, the proposed method is based on a graph-theoretic approach and assumes only a knowledge of the system’s structure. This makes the suggested approach particularly well suited to study large scale systems or systems with unknown parameters, as may be the case during a conception stage.     

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.     

State estimation for networked control systems using fixed data rates

This paper investigates state estimation for linear time-invariant systems where sensors and controllers are geographically separated and connected via a bandwidth-limited and errorless communication channel with the fixed data rate. All plant states are quantised, coded and converted together into a codeword in our quantisation and coding scheme. We present necessary and sufficient conditions on the fixed data rate for observability of such systems, and further develop the data-rate theorem. It is shown in our results that there exists a quantisation and coding scheme to ensure observability of the system if the fixed data rate is larger than the lower bound given, which is less conservative than the one in the literature. Furthermore, we also examine the role that the disturbances have on the state estimation problem in the case with data-rate limitations. Illustrative examples are given to demonstrate the effectiveness of the proposed method.     

Homogeneous dynamical systems theory

We study controlled homogeneous dynamical systems and derive conditions under which the system is perspective controllable. We also derive conditions under which the system is observable in the presence of a control over the complex base field. In the absence of any control input, we derive a necessary and sufficient condition for observability of a homogeneous dynamical system over the real base field. The observability criterion obtained generalizes a well known Popov-Belevitch-Hautus rank criterion to check the observability of a linear dynamical system. Finally, we introduce rational, exponential, interpolation problems as an important step toward solving the problem of realizing homogeneous dynamical systems with minimum state dimensions     

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．     

Characterizing intransitive noninterference for 3-domain security policies with observability

This note introduces a new algorithmic approach to the problem of checking the property of intransitive noninterference (INI) using discrete-event systems (DESs) tools and concepts. INI property is widely used in formal verification of security problems in computer systems and protocols. The approach consists of two phases: First, a new property called iP-observability (observability based on a purge function) is introduced to capture INI. We prove that a system satisfies INI if and only if it is iP-observable. Second, a relation between iP-observability and P-observability (observability as used in DES) is established by transforming the automaton modeling a system/protocol into an automaton where P-observability (and, hence, iP-observability) can be determined. This allows us to check INI by checking P-observability, which can be done efficiently. Our approach can be used for all systems/protocols with three domains or levels, which is sufficient for most noninterference problems for cryptographic protocols and systems.     

基于滑模观测器和广义观测器的故障估计方法

针对受未知干扰影响的一类非线性系统,提出一种基于滑模观测器和广义观测器的执行器故障和传感器故障估计方法.首先通过线性变换将原系统解耦为两个降阶的子系统,其中一个子系统受执行器故障和干扰的影响,另一个含有传感器故障和干扰,进一步将后一个子系统转化为广义系统.对两类子系统分别设计滑模观测器和广义观测器,给出估计误差一致最终有界的条件,得到系统状态和未知干扰的估计值.然后,利用等效输出控制原理重构执行器故障,引入干扰补偿保证重构算法的鲁棒性,再根据广义观测器的结果获得传感器故障的估计值.最后,通过计算机仿真验证了本文方法的有效性.