分布式加权离散事件系统的协同可测性

针对状态转移会携带对应定量信息的分布式系统的可测性问题以加权自动机为模型，研究其协同可测性。首先对分布式加权离散事件系统的强协同可测性和弱协同可测性进行形式化；随后提出基于各分站点观察器构造协同观察器的算法，并得到分布式加权离散事件系统强协同可测性和弱协同可测性的充要条件；最后，给出协同可测性在无线传感器网络系统的一个应用实例。     

模糊离散事件系统的可测性

针对模糊离散事件系统的可测性问题，提出一种基于不可区分串的可测性判定方法。首先引入不可区分串概念以刻画对任一极小可观测事件具有相同的可观察行为；然后构造一个基于极小可观测事件的观察器，建立不可区分串与观察器中非单元循环的一一对应关系，并由此得到模糊可测性的充要条件。同时，也给出一个验证模糊离散事件系统可测性算法。通过实例分析，说明模糊离散事件系统可测性的应用。     

线性控制系统的故障可测性

本文给出了线性控制系统状态和输入，输出故障的数学模型及其故障可测性的充要条件，并进行了证明和物理解释，为控制系统的设计和故障诊断奠定了基础。     

非线性DEDS的周期时间配置与凝着色图

对于用极大极小函数描述的非线性离散事件动态系统(DEDS)，提出一种凝着色图方法。用该方法证明了不同周期时间的数日等于凝点的数日。在此基础上给出了能用状态反馈(独立)配置周期时间的充要条件，解决了与传统线性控制系统极点配置问题完全对应的问题。将该结果应用于线性DEDS，得到了配置域及缩短的周期时间。     

一类强非线性系统共振周期解的渐近分析

强非线性系统经引入参数变换,并在一定的假设条件下,可转化为弱非线性系统．将其解展成为改进的傅立叶级数后,利用参数待定法可方便地求出强非线性系统的共振周期解．研究了Duffing方程的主共振、Van der Pol方程的3次超谐共振和Van der Pol-Mathieu方程的1／2亚谐共振周期解．这些例子表明近似解与数值解非常吻合。     

连续计时离散事件系统监控及其可观性

本文提出了一种带有连续时间变量的离散事件系统(称为计时离散事件系统)结构模型.通过讨论计时语言的性质,如封闭性、可控性以及可观性,研究了计时离散事件系统的监控综合问题,并基于这些性质,分别提出了计时离散事件系统在完全可观与部分可观条件下监控器存在的充要条件.     

线性离散周期奇异系统的可解性与渐近稳定性

讨论了线性离散周期奇异系统初值问题的可解性和渐近稳定性问题.首先分析总结了线性离散变系数奇异系统可解性及其广义状态解的一般概念.在此基础上,定义了线性离散变系数奇异系统的一致渐近稳定性,并通过增加系统维数把线性离散周期奇异系统转化为线性定常奇异系统,从而得到了线性离散周期奇异系统可解和一致渐近稳定的充要条件.     

模型检测规划中的状态之间的可达关系研究

当前,对基于模型检测规划研究的算法中存在大量的冗余计算,一些不可能参与构成解的状态动作序偶被反复筛选.文中给出了一种在不确定规划领域求规划解的新思路:在求规划解之前,找到不确定状态转移系统的状态之间的可达关系,从而根据状态之间的可达关系进行约简.提出了不确定状态转移系统的超图、超图的邻接矩阵和可达矩阵等概念,设计了用超图的邻接矩阵求不确定状态转移系统中状态之间可达关系的方法.利用不确定状态转移系统的超图、超图的邻接矩阵和状态之间的可达关系获得了关于弱规划解、强规划解和强循环规划解的一些重要性质.这些性质是关于一些状态动作序偶是否不可能参与构成弱规划解、强规划解和强循环规划解的结论.通过这些性质可以将大量的状态动作序偶直接去掉,从而大幅度简化求规划解的过程,提高求规划解效率.     

线性切换系统经周期切换渐近稳定性研究

研究一类含有两个子系统的线性切换系统经周期切换渐近稳定问题.首先给出了特殊周期切换,即等时切换下线性切换系统渐近稳定的充要条件;然后将所得结论进行了推广,使之适合于一般的周期切换情形,并结合自适应思想提出了实现系统周期切换的方法,使之能应用于工程实际.特别指出,一个系统可经切换达到二次稳定的充要条件是该系统可经周期切换渐近稳定.对于一类线性切换系统,采用周期切换可使切换信号的设计变得相对简单.仿真结果表明了所提出的方法简洁而有效.     

广义系统的周期解

本文研究了几类广义系统，得出了一类广义线性非齐次系统存在周期解的充要条件，一类广义线性时变系统存在唯一周期解的充分条件；一类广义非线性系统存在周期解的充分条件。     

Detectability of Discrete Event Systems

In this note, we investigate the detectability problem in discrete event systems. We assume that we do not know initially which state the system is in. The problem is to determine the current and subsequent states of the system based on a sequence of observations. The observation includes partial event observation and/or partial state observation, which leads to four possible cases. We further define four types of detectabilities: strong detectability, (weak) detectability, strong periodic detectability, and (weak) periodic detectability. We derive necessary and sufficient conditions for these detectabilities. These conditions can be checked by constructing an observer, which models the estimation of states under different observations. The theory developed in this note can be used in feedback control and diagnosis. If the system is detectable, then the observer can be used as a diagnoser to diagnose the failure states of the system.     

Detectability for Nondeterministic Discrete Event Systems and Its Applications in Medical Diagnosis

In this paper, we extend our previous results on detectability to nondeterministic discrete event systems. Many practical systems are nondeterministic, especially those in biomedicine. Disease models of patients are usually nondeterministic because hardly anything is deterministic in biological systems. The goal is to determine or estimate the current and subsequent states of a system based on a sequence of observations when the initial state of the system is unknown. We say that a system is detectable if one can determine its state after observing some outputs. The observation includes partial event observation and/ or partial state observation. We define four types of detectabilities： strong detectability, （weak） detectability, strong periodic detectability, and （weak） periodic detectability. We derive necessary and sufficient conditions for these detectabilities. These conditions can be checked by constructing an observer, which models the estimation of states under different observation. Furthermore, we apply the results to medical diagnosis by considering a realistic example of diagnosing whether a patient suffers from one of the following five similar diseases ： （ 1 ） rheumatoid arthritis, （2） rheumatic arthritis, （ 3 ） systemic lupus eruthematosus, （4） bony ankylosis, or （ 5 ） spondylitis ankylopoietica.     

Generalized Detectability for Discrete Event Systems

In our previous work, we investigated detectability of discrete event systems, which is defined as the ability to determine the current and subsequent states of a system based on observation. For different applications, we defined four types of detectabilities: (weak) detectability, strong detectability, (weak) periodic detectability, and strong periodic detectability. In this paper, we extend our results in three aspects. (1) We extend detectability from deterministic systems to nondeterministic systems. Such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems. (2) We develop polynomial algorithms to check strong detectability. The previous algorithms are based on an observer whose construction is of exponential complexity, while the new algorithms are based on a new automaton called a detector. (3) We extend detectability to D-detectability. While detectability requires determining the exact state of a system, D-detectability relaxes this requirement by asking only to distinguish certain pairs of states. With these extensions, the theory on detectability of discrete event systems becomes more applicable in solving many practical problems.     

Detectability of networked discrete event systems

Detectability of discrete event systems, defined as the ability to determine the current and subsequent states, is very important in diagnosis, control, and many other applications. So far only detectability of non-networked discrete event systems has been defined and investigated. Non-networked discrete event systems assume that all the communications are reliable and instantaneous without any delays or losses. This assumption is often violated in networked systems. In this paper, we study detectability for networked discrete event systems. We investigate the impact of communication delays and losses on detectability. We define two classes of detectabilities: network detectability for determining the state of a networked discrete event systems and network D-detectability for distinguishing certain pairs of states of the systems. Necessary and sufficient conditions for network detectability and network D-detectability are derived. Methods to check network detectability and network D-detectability are also developed. Examples are given to illustrate the results.     

State estimation and detectability of probabilistic discrete event systems

A probabilistic discrete event system (PDES) is a nondeterministic discrete event system where the probabilities of nondeterministic transitions are specified. State estimation problems of PDES are more difficult than those of non-probabilistic discrete event systems. In our previous papers, we investigated state estimation problems for non-probabilistic discrete event systems. We defined four types of detectabilities and derived necessary and sufficient conditions for checking these detectabilities. In this paper, we extend our study to state estimation problems for PDES by considering the probabilities. The first step in our approach is to convert a given PDES into a nondeterministic discrete event system and find sufficient conditions for checking probabilistic detectabilities. Next, to find necessary and sufficient conditions for checking probabilistic detectabilities, we investigate the “convergence” of event sequences in PDES. An event sequence is convergent if along this sequence, it is more and more certain that the system is in a particular state. We derive conditions for convergence and hence for detectabilities. We focus on systems with complete event observation and no state observation. For better presentation, the theoretical development is illustrated by a simplified example of nephritis diagnosis.     

A physical model for engine control design via role state variables

The present paper describes a model representation of the multi-cyclic phenomena of a multi-cylinder engine system. The model is simplified for the implementation of a practical engine controller. The simplified model is described by physically meaningful state variables, which enables controller designers to effectively consider practical objectives and constraints. The proposed approach consists of two steps. First, an approximate analytical discrete-crank angle model, which is a periodic state equation, is derived from the gas equations, the conservation laws, and the motion dynamics. Second, the concept of role state variables is proposed to transform the periodic state equation into a time-invariant state equation. The stabilizability and detectability of the time-invariant state equation are shown to be equivalent to those of the periodic state equation. The time-invariant state equation is used to design cold start feedforward and feedback controllers.     

A note on the maximal solution of the periodic Riccati equation

The periodic symmetric solutions of the periodic Riccati differential equation associated with the filtering problem are considered by the authors. It is proven that, under the sole assumption of detectability, there exists a maximal solution. Moreover, such a solution turns out to be strong, i.e. the characteristic multipliers of the associated closed-loop system belong to the closed unit disk. The proof relies on an iterative linearization technique, which calls for a sequence of periodic Lyapunov equations. Similar results are given for the minimal solution     

A simulation analysis of the detectability of understory burns in miombo woodlands

The miombo woodlands of southern Africa are one of the most extensively burned biomes in the tropics. The detectability of understory burns in these woodlands was assessed with a sensitivity analysis approach, based on a hybrid geometrical-optical radiative transfer model. Model input data were obtained from a variety of sources, including field biometry and spectroradiometry, and satellite data. The effects of variable tree percent cover, leaf area index, stand density, burn scar age, illumination and observation geometry, and spectral region, were taken into account. Detectability of understory burns was defined as the spectral separability of burned and unburned understory, measured with the Jeffries-Matusita distance, for all possible combinations of the green, red, and near-infrared channels of the Moderate Resolution Imaging Spectrometer (MODIS) sensor. Single channels, or pairwise combinations of channels perform poorly at detecting understory burns, but a large improvement in detectability is obtained for the combination of the three spectral domains. The detectability of understory burns is largely insensitive to the effects of stand structure and illumination/observation geometry, and depends primarily on burn scar age. Our results agree with those of previous satellite-based studies of burns scar detectability in African savanna woodlands.     

周期黎卡提微分方程正定解的存在性

讨论了标准的周期黎卡提微分方程,给出了其存在埃尔米特周期正定（HPPD）解的一个完整的充分必要条件。准确地说,在经过一个适当的状态空间基底变换后该条件通过能稳性和能检测性概念表述。结果表明,当HP－PD解存在时,它或者是唯一的,或者有无限多个。这一结果可以看作是Richardson和Kwong的结果对周期时变情况的扩展。     

Weak detectability and the linear-quadratic control problem of discrete-time Markov jump linear systems

The paper deals with the stochastic concepts of weak detectability and weak observability for Markov jump linear systems, which is an special class of composite linear systems. The concepts are explored here to strengthen the similarities with the corresponding concepts of deterministic detectability and observability. We introduce a collection of matrices, referred to as the observability matrices. We show that weak observability is equivalent to full rank of each matrix in the set of observability matrices. In addition, we present a stochastic counterpart of the well known result on the invariance of trajectories within non-observable subspaces. These characterizations allow us to clarify the relationship between weak detectability and mean square detectability and to provide a testable condition for weak detectability. Relying on the assumption of weak detectability, we develop a method for solving the linear quadratic problem that is based on iterations of uncoupled algebraic Riccati equations, which converges to the solution of the coupled algebraic Riccati equation if and only if the system is mean-square stabilizable. Numerical examples are included.