一类时滞系统的函数观测器设计

针对一类状态变量中含有时滞的线性系统,提出了函数观测器设计的一种参数方法。给出了函数观测器存在的充要条件。基于Lyapunov稳定理论和广义Sylvester矩阵方程的完全参数化解,给出了时滞系统函数观测器设计算法。两个数值例子说明了提出算法的简单性、有效性。该方法提供了进一步满足其他性能要求的设计自由度。     

A New Observer‐Type Consensus Protocol for Linear Multi‐Agent Dynamical Systems

The consensus problem is investigated in this paper for a class of multi‐agent systems with general linear node dynamics and directed communication topologies. A new distributed observer‐type consensus protocol is designed based only on the relative output measurements of neighboring agents. Compared with existing observer‐type protocols, the one presented here does not require information about the relative states of the observers. Tools from small gain theory and matrix analysis, some sufficient conditions are obtained for achieving consensus in such multi‐agent systems where the underlying network topology contains a directed spanning tree. Finally, some numerical examples including an application in low‐Earth‐orbit satellite formation flying are provided to illustrate the theoretical results.     

Minimal unknown-input functional observers for multi-input multi-output LTI systems

Designing minimum possible order (minimal) disturbance-decoupled proper functional observers for multi-input multi-output (MIMO) linear time-invariant (LTI) systems is studied. It is not necessary that a minimum-order unknown-input functional observer (UIFO) exists in our proposed design procedure. If the minimum-order observer cannot be attained, the observer's order is increased sequentially through a recursive algorithm, so that the minimal order UIFO can be obtained. To the best of our knowledge, this is the first time that this specific problem is addressed. It is assumed that the system is unknown-input functional detectable, which is the least requirement for the existence of a stable UIFO. This condition also is a certificate for the convergence of our observer's order-increase algorithm. Two methodologies are demonstrated to solve the observer design equations. The second presented scheme, is a new design method that based on our observations has a better numerical performance than the first conventional one. Numerical examples and simulation results in the MATLAB/Simulink environment describe the overall observer design procedure, and highlight the efficacy of our new methodology to solve the observer equations in comparison to the conventional one.     

Observer Design for Linear Singular Time-delay Systems

Two kinds of observers for linear singular time-delay systems,namely functional ob- servers and full-order observers,are considered in this paper.For the former,observers with and without internal delay are considered.For the latter,observers without internal delay is given.The corresponding design steps for various observers,which are all normal linear time-delay systems,are presented.Numerical examples are given to illustrate the methods.     

线性奇异时滞系统的观测器设计

Two kinds of observers for linear singular time-delay systems, namely functional observers and full-order observers, are considered in this paper. For the former, observers with and without internal delay are considered. For the latter, observers without internal delay is given. The corresponding design steps for various observers, which are all normal linear time-delay systems, are presented. Numerical examples are given to illustrate the methods.     

Open‐Loop Functional Observer and State Feedback for Linear Systems Using Multirate Output Sampling

In this paper, the problem of estimating a linear functional of the state vector is considered in order to implement a feedback control law for discrete‐time linear multivariable systems. The proposed method is based on multirate sampling of the plant output. We give necessary and sufficient conditions for the existence of the functional observer, and propose a functional observer with the minimal number of output samples. In this work, the control law is implemented using the output samples, thus this methodology is more practical than state based techniques. A numerical example is considered to illustrate the procedure and highlight the advantages of the proposed method.     

A Relaxed Gradient Based Algorithm for Solving Extended Sylvester‐Conjugate Matrix Equations

In this paper, a relaxed gradient based algorithm for solving extended Sylvester‐conjugate matrix equations by considering a relaxation parameter is proposed. The convergence analysis of the algorithm is investigated. Theoretical analysis shows that the new method converges under certain assumptions. A numerical example is given to illustrate effectiveness of the proposed method and to test its efficiency compared with an existing one.     

一类线性不确定组合系统的鲁棒控制器和观测器设计*

本文研究了一类带有结构不确定性的线性组合系统的鲁控制器和观测器设计问题，文中给出一种设计分散控制器和分散观测器的方法，其中状态反馈增益 观测器增益阵由两个黎卡提议方程的解给出。     

New Sampling Mode For Linear Time‐Varying Systems

It is proved in this paper that the nonequidistant periodic sampling pattern and zero‐order hold operations do not change the controllability and observability of time variant linear systems during the procedure of discretization for digital control. This result is an extension of the corresponding result for time invariant cases presented in [5].     

Robust State‐and‐Disturbance Observer Design for Linear Non‐minimum‐phase Systems

When there are external disturbances acting on the system, the conventional Luenberger observer design for state estimation usually results in a biased state estimate. This paper presents a robust state and disturbance observer design that gives both accurate state and disturbance estimates in the face of large disturbances. The proposed robust observer is structurally different from the conventional one in the sense that a disturbance estimation term is included in the observer equation. With this disturbance estimation term, the robust observer design problem is skillfully transformed into a disturbance rejection control problem. We then can utilize the standard H_∞ control design tools to optimize the robust observer between the disturbance rejection ability and noise immune ability. An important advantage of the proposed robust observer is that it applies to both minimum‐phase systems and non‐minimum phase systems.     

单输入/单输出非线性系统的状态观测器设计*

本文提出了一类非线性系统的状态观测器设计方法，针对单输入／单输出非线性系统，首先通过非线性状态变换，把原非线性系统变换成简单的中间非线性模型；然后对该简单的中间非线性模型设计稳定的常增益状态观测器，从而经状态逆变换得到原非一系统的非线性状态探测器，最后通过一倒立摆非线性系统的仿真研究说明了该方法的有效性和可行性。     

Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.     

Estimation of Multi‐Order Spectra for Nonlinear Closed‐Loop Systems

In this paper, a multi‐order spectra estimation method is proposed for a nonlinear closed‐loop system based on the Volterra series. Owing to the correlation between the noise and the input, the estimation accuracy is poor when the nonlinear spectra of the plant is obtained using the traditional estimation method. In order to overcome this problem, a two‐step scheme is used to estimate the multi‐order spectrum of a nonlinear system operating in closed‐loop. Firstly, the generalized frequency response functions (GFRFs) from the reference signal to the input of the plant are estimated, and they are used to simulate the noise‐free input spectra of the plant. Secondly, the GFRFs of the controlled plant are estimated using the noise‐free input spectra and the output spectra. Because the GFRFs are multidimensional functions, the required amount of calculation for the estimation is very large. To reduce computational complexity, a simplified GFRF model is adopted to estimate the multi‐order nonlinear spectrum of the plant. In this model, the GFRF is transformed to a one‐dimensional function. Two simulation experiments are provided to illustrate the proposed approach.     

Observer‐Based Consensus Tracking for Nonlinear Multi‐Agent Systems With Intermittent Communications

This paper addresses the observer‐based consensus tracking problem of multi‐agent systems with intermittent communications. The agent dynamics are modeled as general linear systems with Lipschitz nonlinearity. Under the assumption that each agent can intermittently share its relative output with neighbors, a class of an observer‐type protocol is proposed, and the consensus tracking problem can be converted further into the stability problem of the nonlinear switching systems. Using a combined tool from M matrix theory, switching theory and the averaging approach, a multi‐step algorithm is presented to construct the observer gains and protocol parameters, and the sufficient criteria established not only can ensure the state estimates convergence to the real values but also can guarantee the follower states synchronize to those of the leader. The obtained results reveal the relationships among the communication rate, the convergence rate, and the dwell time of switching topologies. Finally, the theoretical findings are validated by a numerical example.     

Event‐Based Consensus Controller for Linear Multi‐Agent Systems Over Directed Communication Topologies: A Co‐Design Approach

The paper addresses the distributed event‐triggered consensus problem in directed topologies for multi‐agent systems (MAS) with general linear dynamic agents. A co‐design approach is proposed to determine parameters of the consensus controller and its event‐triggered mechanism (ETM), simultaneously. This approach guarantees asymptotic stability along with decreasing data transmission among agents. In the proposed event‐based consensus controller, each agent broadcasts data to the neighbors only at its own triggering instants; this differs from previous studies in which continuous data streams among agents were required. Furthermore, the proposed control law is based on the piecewise constant functions of the measurement values, which are updated at triggering instants. In this case the control scheme decreases the communication network usage, energy consumption, and wear of the actuator. As a result, it facilitates distributed implementation of the proposed consensus controller for real‐world applications. A theorem is proved to outline sufficient conditions to guarantee the asymptotic stability of the closed‐loop system with the event‐based consensus controller. Another theorem is also proved to show the Zeno behavior exclusion. As a case study, the proposed event‐based controller is applied for a diving consensus problem to illustrate the effectiveness of the method.     

不确定广义系统的降阶H-infinity控制器设计

研究基于函数观测器的不确定广义系统的降阶H-infinity控制器设计问题. 首先提出了基于严格线性矩阵不等式的不确定广义系统H-infinity控制的充分条件, 并用于状态反馈H-infinity控制设计. 然后对所得控制增益进行降阶观测, 基于广义Sylvester矩阵方程的显式通解, 考虑系统的H-infinity性能约束, 提出了降阶输出反馈控制器的参数化设计方法.     

State and Unknown Input H∞ Observers for Discrete‐Time LPV Systems

This paper proposes state and unknown input (UI) observers for linear parameter varying (LPV) systems affected by UI and perturbations in both state and measurement equations. The estimation is done by minimizing the L₂ transfer between the perturbations and the state estimation error (H_∞‐observation). The originality of the paper is to provide a generalization of existing works, specially by relaxing an assumption on systems matrices, widely used for UI decoupling. After giving the main results, some examples illustrate the theoretical contributions and give comparisons to former publications.     

EFDEX: A Knowledge-Based Expert System for Functional Design of Engineering Systems

This paper presents a knowledge-based system, ‘EFDEX’, the Engineering Functional Design Expert, which was developed using an expert system shell, CLIPS 6.1, to perform intelligent functional design of engineering systems. On the basis of a flexible, causal and hierarchical functional modeling framework, we propose a knowledge-based functional reasoning methodology. By using this intelligent functional reasoning strategy, physical behavior can be reasoned out from a desired function or desired behavior, and inter-connection of these behaviors is possible when there is compatibility between the functional output of one and the corresponding functional requirement (e.g. driving input) of the next one. In addition, a complicated, desired function which cannot be matched with the functional output of any behavior after searching the object-oriented behavior base, will be automatically decomposed into less complex sub-functions by means of relevant function decomposition rules. An intelligent system for the functional design of an automatic assembly system provides an application of this intelligent design environment, and a demonstration of its methodology. In this paper, a knowledge-based functional representation scheme which integrates two popular AI representation techniques (object-oriented representation and rule-based representation) is also proposed as a prelude to a knowledge-based functional design system     

一般模型2-D系统的观测器设计理论

该文讨论了2-D一般模型(2DGM)在标准边界条件下的渐近观测器的存在性条件及其设计问题.为此,首先将由Bisiacco等人在1985年发展起来的相应于对角边界条件的2-D、渐近稳定性理论推广到了具有标准边界条件的2-D一般模型.在此基础上,借助于局部能控性概念,建立了一系列十分类似于1-D情形的观测器的存在条件,从这些存在条件出发也可以得到相应的观测器设计算法,最后还得出了2DGM的分离性定理.     

Output Consensus of Heterogeneous Linear Multi‐agent Systems Subject to Different Disturbances

This paper investigates the output consensus problem of heterogeneous linear multi‐agent systems with individual agents subject to different disturbances. A distributed control law based on internal reference models and dynamic output feedback is presented for output consensus. It is shown that the embedded internal reference models of agents can achieve consensus to a common trajectory which is determined by the underlying system topology and the initial states of the internal reference models. Then a necessary and sufficient condition is presented for output consensus of heterogeneous linear multi‐agent systems. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed control laws.