D-homomorphisms and atomic σ-complete boolean D-posets

We study observables as σ-D-homomorphisms defined on Boolean D-posets of subsets into a Boolean D-poset. We show that given an atomic σ-complete Boolean D-poset ? with the countable set of atoms there exist a σ-complete Boolean D-poset of subsets ? and a σ-D-homomorphism h from ? onto ?, more precisely we can choose ? = ?(?), which gives an analogy of the Loomis–Sikorski representation theorem for Boolean σ-algebras. We show also that any atomic σ-complete Boolean D-poset with the countable set of atoms is the range of a σ-homomorphism defined on a σ-complete Boolean D-poset of fuzzy sets which gives another type of the Loomis–Sikorski theorem.     

一种演化超图文法到状态转移系统的映射方法

运用模型检测技术验证动态演化的正确性,是近年来软件体系结构动态演化研究领域面临的一个挑战.然而,当前的方法很少考虑软件体系结构动态演化时的相关条件.针对该问题,提出用条件状态转移系统表示软件体系结构动态演化的状态模型,将软件体系结构超图映射为状态,演化规则运用映射为条件状态转移关系,给出软件体系结构动态演化的条件超图文法到条件状态转移系统的映射方法以及相应的实现算法,实现了软件体系结构动态演化的条件状态转移系统的构建,并证明了在该映射方法下,软件体系结构动态演化条件超图文法与条件状态转移系统的互模拟等价.最后通过案例分析,运用该方法以及模型检测技术,验证了软件体系结构动态演化的相关性质,从而验证了该方法的有效性.     

Representation of conditional probability on a quantum logic

 In this paper we describe conditional probabilities as difference set. The main idea is that a system is in same state and from this state is can get to another state if there are fulfield some properties. In other words we have a partial binary operation ⊖ such that the operation ⊖ can be interpreted as a change of a state. If we put some logical questions about change of states on this we get the structure which is called a difference set.     

Recognition algorithm for the state of the queuing system based on theory of systems with random jump structure

A problem of constructing a recognition algorithm for the state of the queuing system based on inaccurate measurements is considered. The system has a finite number of states, with their dynamics described by a conditional Markov chain. Optimal and approximately optimal solutions based on the theory of systems with random jump structure are found. An example that uses the proposed approach is given, where the approximately optimal recognition algorithm for the state of a military facility being destroyed and then restored again several times in the course of military activity.     

AN APPROXIMATE DIFFERENTIAL STRUCTURE FOR ERROR COVARIANCE IN NONLINEAR DYNAMICAL SYSTEMS

Abstract

A differential structure for the error covariance matrix is obtained. The starting point of the investigation is the state estimator obtained using Kailath's (1970) innovations approach based on Doob's (1953) theorems on conditional expectations and martingales. The approximate error covariance matrix could be solved a priori since it is independent of the observation process. Also the steady state solution could provide an estimate of the gain matrix in a stochastic approximation scheme.     

Approximate solution to multichain queueing networks with state dependent service rates

An approximation scheme for solving non-product form queueing networks with multiple chains and state dependent service rates is described. Estimates of the steady state probability distribution are obtained using less computational requirements than the standard solution techniques.The approximation scheme is based on a property called chain conditional balance, which leads to a decomposition of the global balance equations into smaller sets of equations. A technique for combining conditional distributions is examined and used to combine the solutions of conditional balance equations into the final estimates. Expressions for the storage and computational requirements of the approximation algorithm are given and an example is provided.An error analysis is described in which the approximation is tested on a large number of randomly generated queueing networks. The experimental results indicate that the approximation yields good estimates of the steady state distribution, as well as several important performance measures of these networks.     

Constructing the dependency structure of a multiagent probabilisticnetwork

A probabilistic network consists of a dependency structure and corresponding probability tables. The dependency structure is a graphical representation of the conditional independencies that are known to hold in the problem domain. We propose an automated process for constructing the combined dependency structure of a multiagent probabilistic network. Each domain expert supplies any known conditional independency information and not necessarily an explicit dependency structure. Our method determines a succinct representation of all the supplied independency information called a minimal cover. This process involves detecting all inconsistent information and removing all redundant information. A unique dependency structure of the multiagent probabilistic network can be constructed directly from this minimal cover. The main result is that the constructed dependency structure is a perfect-map of the minimal cover. That is, every probabilistic conditional independency logically implied by the minimal cover can be inferred from the dependency structure and every probabilistic conditional independency inferred from the dependency structure is logically implied by the minimal cover     

Regulation of nonlinear systems using conditional integrators

This paper studies the regulation of nonlinear systems using conditional integrators. Previous work introduced the tool of conditional integrators that provide integral action inside a boundary layer while acting as stable systems outside, leading to improvement in transient response while achieving asymptotic regulation in the presence of unknown constant disturbances or parameter uncertainties. The approach, however, is restricted to a sliding mode control framework. This paper extends this tool to a fairly general class of state feedback control laws, with the stipulation that we know a Lyapunov function for the closed‐loop system. Asymptotic regulation with improvement in transient response is done by using the Lyapunov redesign technique to implement the state feedback control as a saturated high‐gain feedback and introducing a conditional integrator to provide integral action inside a boundary layer. Improvement in the transient response using conditional integrators is demonstrated with an experimental application to the pendubot. Copyright © 2005 John Wiley & Sons, Ltd.     

On the state estimation for non-linear dynamic systems †

The object of this paper is to present an approximate technique for state estimation of non-linear dynamical systems under noisy observations. The conditional cumulant is introduced, by which the conditional probability density can be characterized. A set of dynamical equations satisfied by conditional cumulants is derived, and an approximate method is proposed for computing the cumulants. The relation of the cumulant method to the stochastic linearization technique is also discussed. Finally the state estimation problem for linear stochaatic system with state-dependent disturbance is solved to illustrate the use of the Gaussian approximation.     

非高斯噪声下输出残差或状态估计误差的熵研究

基于非Gaussian噪声线性定常控制系统,通过控制滤波器输出残差或状态估计误差的条件概率密度函数形状来建立有效的滤波设计算法,创建滤波器输出残差或状态估计误差的条件概率密度函数的统一表现形式。利用复合概率密度函数的关系对残差或状态估计误差的条件概率密度函数的近似来实现非高斯残差的高斯化或相应的熵最小化。     

Modeling threshold conditional heteroscedasticity with regime-dependent skewness and kurtosis

Construction of nonlinear time series models with a flexible probabilistic structure is an important challenge for statisticians. Applications of such a time series model include ecology, economics and finance. In this paper we consider a threshold model for all the first four conditional moments of a time series. The nonlinear structure in the conditional mean is specified by a threshold autoregression and that of the conditional variance by a threshold generalized autoregressive conditional heteroscedastic (GARCH) model. There are many options for the conditional innovation density in the modeling of the skewness and kurtosis such as the Gram-Charlier (GC) density and the skewed-t density. The Gram-Charlier (GC) density allows explicit modeling of the skewness and kurtosis parameters and therefore is the main focus of this paper. However, its performance is compared with that of Hansen’s skewed-t distribution in the data analysis section of the paper. The regime-dependent feature for the first four conditional moments allows more flexibility in modeling and provides better insights into the structure of a time series. A Lagrange multiplier (LM) test is developed for testing for the presence of threshold structure. The test statistic is similar to the classical tests for the presence of a threshold structure but allowing for a more general regime-dependent structure. The new model and the LM test are illustrated using the Dow Jones Industrial Average, the Hong Kong Hang Seng Index and the Yen/US exchange rate.     

离散随机模型降阶的最小条件信息损失方法

针对随机系统的模型降阶问题,从分析离散线性随机状态方程模型中的条件信息描述机制入手,讨论了模型状态集聚过程中系统的平均条件信息损失.运用在模式识别领域中获得成功应用的最小信息损失准则得出了一种新的模型降阶信息论方法———基于状态集聚的最小条件信息损失方法,并讨论了降阶模型阶次的选择.分析表明,当原系统是渐近稳定时,由该方法得出的降阶模型也是渐近稳定的.该方法运用简单,仿真研究也表明由该方法得出的降阶模型具有良好的近似性能.     

Distributed MPC of polytopic uncertain systems: handling quantised communication and packet dropouts

In this paper, we study the distributed model predictive control (MPC) of polytopic uncertain systems with quantised communication and packet dropouts. The model of the whole plant is divided into a certain number of incomplete subsystems. Due to the nature of the distributed control structure, there is generally a lack of information about the state of the overall system. Each subsystem shares its information with neighbour subsystems via reliable connection. Distributed MPC controllers are designed for each subsystem by solving the linear matrix inequalities optimisation problem. The distributed state feedback laws are quantised and transmitted via communication network. An iterative algorithm is presented to make coordination among distributed state feedback laws. The communication is assumed to be affected by random packet dropouts in a representation of Bernoulli distributed white sequences with known conditional probabilities. A case study is carried out to demonstrate the effectiveness of the proposed distributed MPC technique.     

广义随机系统的集值滤波

在具有控制输入和动态噪声与观测噪声相关的情况下,给出线性随机系统的集值滤波方程;利用矩阵分解和系统变换的技巧,得到广义随机系统的集值滤波方程.这种状态估计方法适用于初始状态均值位于一个凸集之中的随机系统.与传统Kalman滤波产生单个条件分布不同,这里的集值滤波给出一个条件分布的凸集.     

On the iterated forms of Kalman filters using statistical linearization

The extended Kalman filter (EKF) is a suboptimal estimator of the conditional mean and covariance for nonlinear state estimation. It is based on first order Taylor series approximation of nonlinear state functions. The unscented Kalman filter (UKF) and the ensemble Kalman filter (EnKF) are suboptimal estimators that are termed as Jacobian free because they do not require the existence of the Jacobian of the nonlinearity. The iterated form of EKF is an estimator of the conditional mode that employs an approximate Newton–Raphson iterative scheme to solve the maximization of the conditional probability density function. In this paper, the iterated forms of UKF and EnKF are presented that perform Newton–Raphson iteration without explicitly differentiating the nonlinear functions. The use of statistical linearization in iterated UKF and EnKF is a nondifferentiable optimization method when the measurement function is nonsmooth or discontinuous. All three iterated forms can be shown to be conditional mean estimators after the first iteration. A simple numerical example involving continuous and discontinuous measurment functions is included to evaluate the performance of the algorithms for the estimation of conditional mean, covariance and mode. A batch reactor simulation is shown for estimating both the states and unknown parameters.     

Conditional central algorithms for worst case set-membershipidentification and filtering

This paper deals with conditional central estimators in a set membership setting. The role and importance of these algorithms in identification and filtering is illustrated by showing that problems like worst case optimal identification and state filtering, in contexts in which disturbances are described through norm bounds, are reducible to the computation of conditional central algorithms. The conditional Chebyshev center problem is solved for the case when energy norm-bounded disturbances are considered. A closed-form solution is obtained by finding the unique real root of a polynomial equation in a semi-infinite interval     

Modelling of the interframe dependence in an HMM using conditional Gaussian mixtures

This paper investigates the modelling of the interframe dependence in a hidden Markov model (HMM) for speech recognition. First, a new observation model, assuming dependence on multiple previous frames, is proposed. This model represents such a dependence structure with a weighted mixture of a set of first-order conditional Gaussian densities, each mixture component accounting for a specific conditional frame. Next, an optimization in choosing the conditional frames/segment is performed in both training and recognition, thereby helping to remove the mismatch of the conditional segments due to different observation histories. An EM (Expectation–Maximization) iteration algorithm is developed for the estimation of the model parameters and for the optimization over the dependence structure. Experimental comparisons on a speaker-independent E-set database show that the new model, without optimization on the dependence structure, achieves better performance than the standard HMM, the bigram HMM and the linear-predictive HMM, all in comparable or smaller parameter sizes. The optimization over the dependence structure leads to further improvement in the performance.     

基于联合条件随机场的移动机器人多目标跟踪

通过将目标与观测数据之间的数据关联抽象为标记序列,为移动机器人的多目标跟踪提出了一种具有多层次结构的联合条件随机场(joint conditional random field,JCRF).JCRF包括联合数据关联和运动目标状态估计两层随机场,不仅在联合数据关联中可以融合目标的形状信息和运动信息以提高目标跟踪的稳定性,而且可以同时进行目标检测与目标跟踪.利用JCRF模型,对基于激光距离传感器的多目标跟踪进行了研究,通过从激光距离传感器信息中分割出候选目标区域,采用匹配树降低标记序列的状态空间.在移动机器人平台上进行实验,结果表明,基于JCRF的多目标跟踪具有良好的精度、稳定性和实时性.