Modeling Discrete Event Systems With Faults Using a Rules-based Modeling Formalism

Obtaining accurate models of systems which are prone to failures and breakdowns is a difficult task. In this paper we present a methodology which makes the task of modeling failure prone discrete event systems (DESs) considerably less cumbersome, less error prone, and more user-friendly. The task of obtaining commonly used automata models for DESs is non-trivial for most practical systems, owing to the fact that the number of states in the commonly used automata models is exponential in the number of signals and faults. In contrast a model of a discrete event system, in the rules based modeling formalism proposed by the co-authors of this paper, is of size polynomial in the number of signals and faults. In order to model failures, we augment the signals set of the rules based formalism to include binary valued fault signals, the values representing either a non-faulty or a faulty state of a certain failure type. Addition of new fault signals requires introduction of new rules for the added fault signal events, and also modification of the existing rules for non-fault events. The rules based modeling formalism is further extended to model real-time systems, and we apply it to model delay-faults of the system as well. The model of a failure prone DES in the rules based can automatically be converted into an equivalent (timed)-automaton model for a failure analysis in the automaton model framework.     

Performance Optimization of a Class of Discrete Event Dynamic Systems Using Calculus of Variations Techniques

We explore an approach involving the use of calculus of variations techniques for discrete event dynamic system (DEDS) performance optimization problems. The approach is motivated by the observation that such problems can be described by separable cost functions and recursive dynamics of the same form as that used to describe conventional discrete-time continuous-variable optimal control problems. Three important difficulties are that DEDS are generally stochastic, their dynamics typically involve max and min operations, which are not everywhere differentiable, and the state variables are often discrete. We demonstrate how to overcome these difficulties by applying the approach to a transportation problem, modeled as a polling system, where we are able to derive an explicit and intuitive analytic expression for an optimal control policy.     

一类离散动力系统的稳定性

研究一类作 为基因选择模 型的离散动力系 统ｙ ｎ ＋ １ ＝ ｙｎ ｅｂ（ １ － ２ ｙ ｎ － ｋ ）１－ ｙｎ ＋ ｙｎ ｅｂ（ １ － ２ ｙ ｎ － ｋ ） ,　ｎ ＝ ０,１,… ,的稳定性 ,其中 ｂ∈（０,∞）, Ｋ∈ ｛１,２,…｝     

一类非线性离散系统的同宿解的存在性

应用临界点理论讨论一类二阶非线性离散系统在一定条件下非零同宿解的存在性,得到一个非零同宿解存在性的条件.     

一类二阶离散哈密尔顿系统的周期解的多重性

基于变分法,运用三临界点定理,得到了一类有小强迫项的二阶离散哈密尔顿系统的周期解的多重性,推广了现有文献的相关结果,并给出例子加以说明.     

一类离散系统的全局渐近稳定性

本文对一类离散系统xi 1=T(xi) ,i=0 ,1 ,2…给出全局渐近稳定的判据 ,这些判据推广了文 [1 3]中的结论 ,使得应用更为广泛 .     

Rates of Convergence of Ordinal Comparison for Dependent Discrete Event Dynamic Systems

Recent research has demonstrated that ordinal comparison, i.e., comparing relative orders of performance measures, converges much faster than the performance measures themselves do. Sometimes, the rate of convergence can be exponential. However, the actual rate is affected by the dependence among systems under consideration. In this paper, we investigate convergence rates of ordinal comparison for dependent discrete event dynamic systems. Although counterexamples show that positive dependence is not necessarily helpful for ordinal comparison, there does exist some dependence that increases the convergence rate of ordinal comparison. It is shown that positive quadrant dependence increases the convergence rate of ordinal comparison, while negative quadrant dependence decreases the rate. The results of this paper also show that the rate is maximized by using the scheme of common random numbers, a widely-used technique for variance reduction.     

一类具有分离变量的非线性离散系统的镇定控制器

在控制理论和控制工程中，镇定控制器的设计是一个经典问题。许多有关这个问题的结论一般都是针对线性系统。对于非线性系统，很少见到有构造性结果能用于控制工程中。本针对一类广泛的非线性控制系统，我们构造了一些控制器，这些判据在工程实际问题中将具有一定的指导意义。     

一类离散T-S模糊广义系统的控制器设计

利用离散广义Lyapunov方法和分段模糊Lyapunov函数并借助子系统的性质,解决了一类离散T-S广义模糊系统的模糊控制及模糊状态观测器设计问题,得出了离散T-S模型广义系统其极值子系统的基础上设计出的新的模糊控制器和模糊状态观测器.     

图论在离散事件动态系统中的应用

运用图论方法和极大代数方法,研究了非强连通图中的强连通分支的最大圈长平均值与该图的赋权邻接矩阵的特征值之间的关系,并进一步证明了其等价性.     

基于观测器的一类时滞不确定非线性离散系统的鲁棒模糊控制

讨论一类基于Takagi-Sugeno(T-S)模糊模型的具有时滞的不确定非线性离散系统的模糊鲁棒控制问题。在系统状态不可测的情况下。设计模糊观测器。利用LMI方法,得到模糊控制系统鲁棒稳定的充分条件。     

Asymptotic Stability for a Class of Neutral Systems with Discrete and Distributed Time Delays

In this note, the asymptotic stability for a class of neutral systems with discrete time and distributed time delays is considered. Delay-dependent criteria are proposed to guarantee the stability for such systems. Some numerical examples are given to illustrate that our results are less conservative than previous results.     

一类半线性抛物型方程的紧差分格式

本文构造了一类半线性抛物方程初边值问题的紧差分格式．利用离散能量估计证明了差分格式解的存在唯一性、收敛性和无条件稳定性，并给出了在离散L^∞模意义下收敛阶数为O（h^4＋τ^2）．数值例子验证了理论分析结果。     

An Improved Fuzzy Modeling Method for a Class of Multi-Input Non-affine Nonlinear Systems

In this paper, an improved fuzzy modeling method is developed for a class of non-affine nonlinear systems. The idea comes from the concepts of the optimization tools and the Takagi–Sugeno fuzzy modeling technique. Specifically, this method is suitable especially for non-affine nonlinear systems. Two benchmark single-input and one multi-input non-affine nonlinear systems are illustrated to show that the proposed modeling scheme is superior to existing modeling methods.     

一类二维离散动力系统的稳定性与分岔

本文利用正规则型理论讨论了一类二维离散动力系统的动力学性质，分析了其正平衡点的稳定性，并讨论了Neimark—Sacker分岔稳定性与方向。通过数值模拟验证了所得结果的正确性。     

一类离散系统边值问题多个解的存在性

应用临界点理论,获得了一类离散系统边值问题存在多个解的条件.     

Introduction to the Special Issue on Discrete Event Models of Continuous Systems

Automatic control systems rely on models to predict the near future and identification algorithms to adapt the models to changing process behaviour. The traditionally highly complex models of the activated sludge process developed for scientific purposes cannot be identified from on-line measurements and are not suited for process control purposes in their present form. Model decoupling based on the different time scales of the dynamic processes is one possible way of attacking this problem. It allows the implementation of more simple and realistically applicable controllers in combination with predictions based on simplified models in hierarchical control structure. This paper discusses these concepts and presents a reduced order model describing carbonaceous removal, nitrification, and denitrification in a medium time scale (several hours/days). The model parameters are identifiable from available on-line measurements and the dynamic behaviour is verified against computer simulations of the IAWQ activated sludge model no. 1.     

A Characterization of a Certain Class of Compact Metric Spaces

Compact metric spaces χ of such a kind, that ??_f =??(X), are characterized, ??(X) is the σ-field of BOREL sets and ??_f(X) is the field generated by all open subset of X. Our main result is Theorem 5: If χ is a compact metric space, then the following conditions are equivalent:

• 1 ??_f(X) =??(X).
• 2 card (X) ≦x₀ and there are k, m?N such that card (X^(k)) = m.
• 3 There are k, m?N such that χ is homeomorphic to ω^k · m + 1.