近地小行星仅测角相对导航可观性判据

针对近地小行星仅测角相对导航系统的非线性可观测性分析问题,本文基于非线性系统局部弱可观性理论给出了新的可观测性判据.首先,通过分析非线性系统李导数的共有属性,给出了李导数梯度空间的共有子空间.进一步,利用该共有子空间和非线性系统局部弱可观性定义给出了新的可观性判据.经理论证明,该判据适用于非线性系统任意阶李导数,并且给出的可观性结论可与高阶可观性矩阵秩判据的结论等价.与传统的秩判据相比,该判据具有无需进行高阶李导数运算,无需进行高维矩阵运算的优点.因此该判据适合在轨计算,具有一定的工程价值.最后仿真结果验证了可观性判据的有效性.     

网络调度中的能控性与能观性研究

为了研究网络调度对能控性与能观性的影响,对输入、输出通道都存在通信约束的网络控制系统的调度进行建模;利用通信序列表示通道的调度情况,最终将模型转化为离散切换系统;在静态调度下,利用循环不变子空间理论及其相关的性质,给出了网络控制系统能控性、能观性成立的充要条件,并给出了原有控制系统与经网络静态调度后的系统之间能控性、能观性的关系;最后用仿真实例说明了所提结论的正确性。     

Nonlinear unknown input observability and unknown input reconstruction: The general analytical solution

Observability is a fundamental structural property of any dynamic system and describes the possibility of reconstructing the state that characterizes the system from fusing the observations of its inputs and outputs. Despite the effort made to study this property and to introduce analytical criteria capable of verifying whether or not a dynamic system satisfies this property, there is no general analytical criterion to obtain the observability of the state when the dynamics are also driven by unknown inputs. Here, we introduce the general analytical solution of this fundamental open problem, often called the unknown input observability problem. We provide the systematic procedure, based on automatic calculation (differentiation and determination of the matrix rank), which allows us to check the observability of the state even in the presence of unknown inputs. One of the fundamental ingredients to obtain this solution is the characterization of the group of invariance of observability. We have very recently introduced this group, together with a new set of tensor fields with respect to this group of transformations (Martinelli, 2020). The analytical solution of the unknown input observability problem is expressed in terms of these tensor fields. In Martinelli (2020) we provided the solution by restricting our investigation to systems that satisfy a special assumption that is called canonicity with respect to the unknown inputs. Here, after an exhaustive characterization of the concept of canonicity, we also account for the case when this assumption is not satisfied and we provide the general solution. This solution is also provided in the form of a new algorithm. In addition, even in the canonic case dealt with in Martinelli (2020), here we provide a new fundamental result that regards the convergence properties of the solution. Finally, as a consequence of the results obtained here, we also provide the condition to reconstruct the unknown inputs, and, when this condition is not met, what can be reconstructed on the unknown inputs. We illustrate the implementation of the new algorithm by studying the observability properties of a nonlinear system in the framework of visual-inertial sensor fusion, whose dynamics are driven by two unknown inputs and one known input. In particular, for this system, we follow step by step the algorithm introduced by this paper, which solves the unknown input observability problem in the most general case.     

Unknown input observability for discrete-time linear multivariable systems and its application

A new concept of the unknown input observability, namely (r, s ; K) observability, for discrete-time linear multivariable systems is introduced. This concept is an extension of the conventional unknown input observability and reconstructibility. Necessary and sufficient conditions for the (r, s ; K) observability of the given system are derived by introducing a new unobservable subspace and presenting algorithms for obtaining the subspace. It is also shown that these new concepts are closely related to the existence condition of a dead-beat observer for a decentralized control system.     

Duality Properties of Linear Impulsive Systems

Reachability and observability properties of linear switched, impulsive, and switched/impulsive systems have received a great deal of attention over the past decade. The purpose of this paper is to rigorously establish a duality between reachability and observability for linear impulsive systems both in direct system‐theoretic terms as well as in geometric terms. These connections are established using an appropriately defined adjoint system associated with the original impulsive system. The duality between reachability and observability is then used to leverage recent reachability results in order to tighten the relationship between the set of unobservable states and a certain invariant subspace.     

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.     

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 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.     

On the controllability and observability of discrete-time linear time-delay systems

This article studies the controllability and observability of discrete-time linear time-delay systems, so that the two properties can play a more fundamental role in system analysis before controller and observer design is engaged. Complete definitions of controllability and observability, which imply the stabilisability and detectability, respectively, and determine the feasibility of eigenvalue assignment, are proposed for systems with delays in both state variables and input/output signals. Necessary and sufficient criteria are developed to check the controllability and observability efficiently. The proofs are based on the equivalent expanded system, but the criteria only involve the delays and matrices of the same dimension as the original system. Finally, the duality between the suggested controllability and observability is presented.     

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.     

Controllability and observability of state‐dependent switched Boolean control networks with input constraints

This paper investigates the controllability and observability of state‐dependent switched Boolean control networks (SDSBCNs) with input constraints. First, the algebraic form of SDSBCNs is derived via the semi‐tensor product of matrices. Then constrained model‐input‐state (CMIS) matrices are introduced for SDSBCNs with input constraints. On the basis of CMIS matrices, two necessary and sufficient conditions are provided for the controllability and observability. Finally, two examples are given to show the effectiveness of the main results.     

Semilinear observation systems

In this paper, we introduce locally Lipschitz observation systems for nonlinear semigroups and show that they can be represented by an ‘admissible’ nonlinear output operator defined on a suitable subspace. In the semilinear case, this concept fits well to the Lebesgue extension known from linear system theory. For semilinear systems, we show robustness of exact observability near equilibria under locally small Lipschitz perturbations. Finally, we apply our results to a damped nonlinear plate equation and a semilinear thermo-elastic system.     

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.     

Controllability and Observability of Parallel Magnetic Suspension Systems

The controllability and observability of parallel magnetic suspension systems are investigated analytically. A parallel magnetic suspension system has multiple floators and electromagnets driven by a single amplifier. In this paper, the multiplicity is set to an arbitrary counting number n. Parallel systems are classified into four types based on the output of the power amplifier and the connection of the coils. This paper treats three of them: current‐controlled with series‐connected coils; voltage‐controlled with series‐connected coils; and voltage‐controlled with parallel‐connected coils. The conditions of controllability and observability of each system are clarified. The feasibility of parallel magnetic suspension is demonstrated by simulations and experiments.     

Bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control

The paper deals with the problem of stabilization of stationary bifurcation solutions of nonlinear systems via dynamic output feedback.It is emphasized that the parameter of the system is not directly available.We introduce the concepts of uniform observability of the inverse of a function of state and input and N-order-input-to-state bifurcation stability.Based on the concepts,we propose a new method for designing dynamic compensators that guarantee bifurcation stability for the closed-loop system.As an example,we apply the general theory to active control of rotating stall in axial flow compressors by designing a stabilizing dynamic compensator for the three-state Moore-Greitzer model with a class of cubic compressor characteristics.     

Orthogonal projection based subspace identification against colored noise

In this paper, a bias-eliminated subspace identification method is proposed for industrial applications subject to colored noise. Based on double orthogonal projections, an identification algorithm is developed to eliminate the influence of colored noise for consistent estimation of the extended observability matrix of the plant state-space model. A shift-invariant approach is then given to retrieve the system matrices from the estimated extended observability matrix. The persistent excitation condition for consistent estimation of the extended observability matrix is analyzed. Moreover, a numerical algorithm is given to compute the estimation error of the estimated extended observability matrix. Two illustrative examples are given to demonstrate the effectiveness and merit of the proposed method.     

Local observability of invariant dynamics on compact Lie groups with square integrable output map functions

In this work, we give a sufficient algebraic condition for the local observability problem of invariant control systems on compact Lie groups such that the output map is not differentiable. In particular, the usual techniques involving Lie derivatives do not work. Our approach comes from the representation theory. We use the regular representation to construct a bilinear system on the Hilbert space of the square integrable function defined on the group to a finite-dimensional vector space. If this bilinear system is observable, then we prove that the invariant control system is locally observable.     

Observability of Depth Estimation for a Hand‐Eye Robot System

This paper deals with the depth observability problem of a hand‐eye robot system. In contrast to earlier works, this paper presents a complete study of this observability problem. The velocity of the active camera in the hand‐eye robot system is considered as the input. The observability of depth estimation is then related to the velocity of the camera. A necessary and sufficient condition for the types of camera velocities necessary to ensure observability is found. This compensates for the results of earlier works, in which the velocity of camera was estimated. The theory is also verified by both simulations and experiments in this paper. Furthermore, a modified LQ visual servo control law is proposed to vary the weighting matrices so that depth estimation is improved while the level of control performance is still retained.     

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     

On Detectability and Observability of Discrete‐Time Stochastic Markov Jump Systems with State‐Dependent Noise

This paper mainly studies the notions of detectability and observability for discrete‐time stochastic Markov jump systems with state‐dependent noise. Two concepts, called “W‐detectability” and “W‐observability,” for such systems are introduced, and are shown to coincide with the other concepts on detectability and observability reported recently in literature. Moreover, some criteria and interesting properties for both W‐detectability and W‐observability are obtained.