间歇过程基于Dioid代数模型的分析与协调控制研究

针对现有间歇过程模型的不足之处,提出了一种新的间歇过程Dioid代数模型,此模型不仅描述了间歇过程中的离散事件,而且还用于间歇过程的定量分析,在此模型基础上,我们用代数方法研究了间歇过程的协调控制问题。     

IFS与L系统的统一描述语言及其分类

为了更高效地表示分形图形,依据形式语言的文法结构及正则表达式的文法规则,通过引入代数运算,提出了一个能够对L系统和迭代函数系统(IFS)统一描述的语言代数系统。根据语言代数系统产生式的文法规则,将此系统的产生式集划分为五类。结合分形理论,此语言代数系统着重将DOL系统、迭代函数系统(IFS)、带凝聚集迭代函数系统(凝聚IFS)、随机迭代函数系统(IFSP)和再归迭代函数系统(RIFS)等进行描述,同时用此系统的正则表达式方程解将分形吸引子进行代数表示,并给出一些实例。通过实例表明,分形图形可以用该语言代数系统简单、明了、高效地表示。     

网络演算理论及应用研究

网络演算理论是最近发展起来的一种新的网络QoS理论,它是最小加代数(Min-PlusAlgebra)和最大加代数(Max-PlusAlgebra)在网络分析中所取得的一系列应用结果的集合。文章主要对网络演算理论及应用研究进行了全面系统的综述。     

路由网络代数

基于基本网络代数 (BasicNetworkAlgebra ,BNA)和LOTOS/E LOTOS ,该文提出一种适合于分析Inter net路由系统行为的代数系统 .该代数系统称为路由网络代数 (RoutingNetworkAlgebra,RNA) ,它结合了BNA中的并行、串行运算以及LOTOS中的同步并行运算 ,并在此基础提出更适合于描述Internet路由系统行为的选择运算“ ”、协同并行“ ”以及路由网络常量 ,如m×n(路由转发 )、∧ m(分支 )、∨ m(合并 )、⊥ m(下沉 )和┬ m(亚元 ) .通过分析由上述代数运算和路由网络常量构成的路由网络代数模型 ,可以分析路由系统中死锁 (deadlock)和活锁(alivelock)等行为 .为了检验路由网络代数的有效性 ,完成了BGP路由稳定性的实验分析工作 .     

抽象数据类型的双代数结构及其计算

程序语言中的许多抽象数据类型包含了可递归定义的语法构造和可共递归定义的动态行为特征,因此单纯利用代数或共代数难以给出完整的描述.双代数是同一载体集上的代数和共代数对,提供了一种从范畴论的角度探讨抽象数据类型上的语法构造和动态行为关系及性质的可行途径.给出抽象数据类型的双代数结构,并利用代数函子对共代数函子的分配律描述了语法构造与动态行为之间的自然转换关系;利用分配律对共代数和代数函子进行函子化提升,给出一种构造初始代数(或终结共代数)上的共代数(或代数)结构,并将其提升为初始(或终结)λ-双代数的方法.在此基础上,进一步将函子化提升应用于各种递归(包括迭代和原始递归)及共递归函数(包括共迭代和原始共递归)的定义及计算中,并给出相应的计算定律.     

条件事件代数研究综述

综述了条件事件代数理论的原理、主要性质和应用．条件事件代数是一门新兴的解决不确定性、概率性和模糊性推理问题的学科,是在确保规则概率与条件概率相容的前提下,把布尔代数上的逻辑运算推广到条件事件(规则)集合中得到的代数系统,目的是为智能系统中的条件推理建立一个数学基础．该文也对比条件事件代数更一般的逻辑系统——关联事件代数理论进行了介绍．     

基于概念格模型的代数系统应用分析

针对现阶段模式识别与人工智能领域形式化概念分析理论的多样性、复杂性、分类不均衡等各种不足点,对概念格结构以及其代数系统进行了深入分析与比较。依次对认知信息学代数系统、N代数系统以及W代数系统进行了阐述与剖析,对比了各个不同形态概念代数的系统思想与方法特征,并对N代数系统进行了广义概念代数理论形式化证明,为不同领域内概念表达、应用与分析模型的有效构建提供了强有力的知识支撑。     

基于条件事件代数的贝叶斯网的逻辑推理

条件事件代数理论在数据融合系统中有着重要的应用前景,该理论可用来解决不确定性、概率性和模糊性推理问题。条件事件代数是在确保规则与条件概率相容的前提下,把布尔代数上的逻辑运算推广到条件事件(规则)集合中的逻辑代数系统。对于一些特殊的贝叶斯网(如多树型网络)已经有了一些可行的概率推理的算法,但到目前为止,还没有可行的逻辑推理的算法。随着对不确定性知识研究的深入,迫切需要具有逻辑推理的算法。论文介绍了乘积空间条件事件代数的定义和基本性质,提出了基于乘积空间条件事件代数的贝叶斯网的逻辑推理的算法以及应用。     

用于离散事件系统研究的代数方法

dioid 理论(极大代数等)是研究离散事件系统的重要方法.它不仅可以对运行过程做出细致的描述,而且已经开发出一套“线性”系统理论,给深入研究奠定了基础.术文侧重介绍有关代数方法的理论基础与最新发展.     

一种泛逻辑代数系统

文[3]给出了理想状态(广义相关系数h=0.5,广义自相关系数k=0.5)下泛逻辑的形式演绎系统B,证明了此系统是可靠的。该文提出理想状态下(h=k=0.5)泛逻辑学对应的代数系统-UB代数,给出它的一系列性质。证明了UB代数是一个交换剩余半群;进一步证明了U B代数与M V代数、正规FI代数是等价的。     

Performance evaluation of nonlinear weighted T-system

This article deals with the analysis of discrete event systems which can be modelled by timed event graphs with multipliers (TEGMs). These graphs are an extension of weighted T-systems studied in the Petri net literature. These models do not admit a linear representation in (min,?+) algebra. This nonlinearity is due to the presence of weights on arcs. To mitigate this problem of nonlinearity and to apply some basic results used to analyse the performances of linear systems in dioid algebra, we propose a linearisation method of mathematical model reflecting the behaviour of a TEGM in order to obtain a (min,?+) linear model.     

A Dioid Model for Invariant Resource Sharing Problems

This paper proposes a model for invariant resource sharing problems in dioid algebra. A strong motivation for investigating the issue is the absence of a general systematic technique which can be used to tackle these problems. (min, +) constraints have been developed to handle resource sharing in Discrete-Event Dynamic Systems. In particular, the part that can be modeled by a Timed Event Graph induce (min, +)-linear equations which are constrained by the resource availability. The proposed algebraic model has been proved to describe the actual behavior of the systems dealt with. This paper will show two examples of systems that are modeled and controlled by means of this approach.     

DEDS双子模型的等价变换及其应用

提出了ＤＥＤＳ双子模型的等价变换与等价系统,给出了其定义,研究了其主要特性和计算方法,探讨了其在ＤＥＤＳ双子模型的简化、规范化及性能分析方面的应用,文中还给出了等价变换在建模、传函矩阵计算和有关定理证明方面应用的实例。     

Interval analysis and dioid: application to robust controller design for timed event graphs

This paper deals with feedback controller synthesis for timed event graphs, where the number of initial tokens and time delays are only known to belong to intervals. We discuss here the existence and the computation of a robust controller set for uncertain systems that can be described by parametric models, the unknown parameters of which are assumed to vary between known bounds. Each controller is computed in order to guarantee that the closed-loop system behavior is greater than the lower bound of a reference model set and is lower than the upper bound of this set. The synthesis presented here is mainly based on dioid, interval analysis and residuation theory.     

Development of a new dioid algebraic model for manufacturing with the scheduling decision making capability

The dioid algebraic model, which is developed in this paper, captures the discontinuous nature of Discrete-Event Dynamic Systems and has widespread applicational capabilities. As a further improvement over existing dioid algebraic models, decision making capability is introduced to the developed dioid algebraic model. With this new capability, sequencing decisions at each machine can be represented in the model. Furthermore, the developed algebraic model is capable of representing job and resource unavailability, technological constraints, alternative process plans, and is easily modifiable to include new jobs and exclude finished jobs. In a possible application, the model can be used in representing dynamic scheduling problems and can be used as an important part of a real-time control and scheduling scheme of a manufacturing system.     

Modeling and Control of Hybrid Timed Event Graphs with Multipliers Using (Min, +) Algebra

We study a subclass of Petri nets, called hybrid timed event graphs with multipliers, or equivalently, hybrid timed weighted marked graphs, composed of continuous and discrete graphs interconnected among themselves. Such graphs can be modeled by using a particular algebra, called dioid, defined on a set of operators and endowed with the pointwise minimum operation as addition and the composition operation as multiplication. A just in time control method of these graphs based on residuation theory is proposed.     

An algebraic model for performance evaluation of timed event multigraphs

This note demonstrated that a certain class of Petri nets called timed-event multigraphs can be represented as a set of linear equations by using a novel dioid. With this new algebra, some properties are presented in the text. An example is discussed in the end, and an interesting result is computed.     

Modeling and control of high-throughput screening systems

In previous work it has been shown how a max-plus algebraic model can be derived for cyclically operated high-throughput screening systems and how such a model can be used to design a controller to handle unexpected deviations from the predetermined cyclic operation during run-time. In this paper, this approach is extended by modeling the system in a general dioid algebraic setting. Then a feedback controller can be computed using residuation theory. The resulting control strategy is optimal in the sense of the just-in-time criterion, which is very common in scheduling practice.     

Shrinking of Time Petri nets

The problem of the synthesis of time bounds enforcing good properties for reactive systems has been much studied in the literature. These works mainly rely on dioid algebra theory and require important restrictions on the structure of the model (notably by restricting to timed event graphs). In this paper, we address the problems of existence and synthesis of shrinkings of the bounds of the time intervals of a time Petri net, such that a given property is verified. We show that this problem is decidable for CTL properties on bounded time Petri nets. We then propose a symbolic algorithm based on the state class graph for a fragment of CTL. If the desired property “includes” k-boundedness, the proposed algorithm terminates even if the net is unbounded. A prototype has been implemented in our tool Romeo and the method is illustrated on a small case study from the literature.