一类有序样品聚类的动态规划方法

变结构特征的识别在经济计量模型建立中具有重要价值 .本文用动态规划方法讨论了一类社会经济系统模型结构变化点的问题 ,并通过实例进行了验证 .文中引进了线性模型来划分变结构模型 ,并编写出用动态规划方法聚类的计算程序 .大量模拟计算表明该方法实用性强 ,算法简便 ,便于应用 .     

局部区域的最佳脉冲随机控制

本文分析了一类脉冲随机控制模型,用新方法给出了初始状态在某一区域时最佳费用函数的解析表达式,从而构造出一个最佳控制.研究结果表明,该控制结构简单因而便于实际应用.     

一种双寡头垄断Cournot-Puu模型的混沌控制研究

基于非线性动力学的基本原理,研究了经济系统中的双寡头垄断Cournot-Puu模型及其混沌控制方法.Cournot-Puu模型具有双曲线形需求函数和彼此不同的不变边际成本,离散化的差分系统显示出其复杂的非线性、分岔和混沌行为.在此基础上,结合Cournot-Puu模型的基本特征,应用延迟反馈控制方法以及自适应控制方法对该系统的混沌行为进行了研究.在结合实际经济意义的条件下,对该模型的输出进行调整并实现混沌控制.     

纯增益反馈控制律在MF模型中的应用研究

给出蒙代尔-弗莱明模型的动态表述,并证明蒙代尔-弗莱明模型的动态系统具有能控性、能达性、能观性等结构特征.在蒙代尔-弗莱明模型动态系统的基础上对开放经济条件下宏观经济模型的供需均衡问题转化为宏观经济政策的控制律设计问题,得出开放经济条件下宏观经济政策的纯增益反馈控制律的解析解并且对控制律的解析解的政策含义作出阐述.本文...     

一类基于属性变量的DEA模型

系统评价不仅应重视系统的经济特征,还必须重视系统的非经济特征.在评价系统的非经济特征时必须考虑属性变量,即不能以货币衡量的反映系统非经济特征的定量变量.在过去关于DEA的研究中并未涉及到这种变量.本文对属性变量进行了明确的定义,并提出一种基于属性变量的DEA效率评价模型,最后通过实例演示了模型的合理性.     

货币供给动态调控模型及其稳定性

根据我国货币政策传导机制并结合目前经济金融形势,建立了货币供给系统的一般动态模型,为了便于分析系统的稳定性,在此基础上建立前向离散货币供给系统简化模型并用经济控制论的方法分析了系统的稳定性。     

可分解的区间冯·纽曼模型均衡解的存在性

本文研究具有可分解性质的区间冯·纽曼经济系统模型均衡解的存在性,并推导出两个重要而实用的判别定理,为研究不确定性经济系统模型提供了新工具.     

非线性经济增长模型的最优控制问题

研究了带有中性技术进步生产函数边界条件的非线性经济增长模型的最优控制问题.利用Banach空间不动点原理,得到了系统解的存在唯一性,利用Gronwall不等式得到了系统解关于控制序列的连续依赖性,借助于法锥和共轭系统,得到了控制问题最优解存在的必要条件.     

带扩散项单种群模型的精确能控性

本文研究了一类单种群生态模型的精确能控性问题.利用线性化系统的Carleman估计和Kakutani不动点定理,证明了该模型稳态解的局部能控性.它反应了外部控制在种群演变过程中的影响作用.     

基于T-S模型的奇异摄动系统的采样鲁棒H_∞控制

基于T-S模型,对基于采样数据的非线性奇异摄动系统的鲁棒H_∞控制问题进行研究.对于T-S模型中规则后件中的各个局部线性模型,利用"输入滞后"(input delay)方法,将基于采样数据的离散形式的控制律转化为带滞后的连续形式的控制律.在此控制律之下,局部闭环系统成为一个变时滞的连续奇异摄动系统.在对此闭环系统的稳定性和L_2增益特征进行分析的基础上,以LMI的形式给出了满足要求的控制律满足的条件.然后将各个局部线性模型的控制律利用模糊推理方法 "合成"为系统总的控制律.     

Software reliability assessment models based on cumulative bernoulli trial processes

The binomial software reliability growth model (SRGM) contains most existing SRGMs proposed in earlier work as special cases, and can describe every software failure-occurrence pattern in continuous time. In this paper, we propose generalized binomial SRGMs in both continuous and discrete time, based on the idea of cumulative Bernoulli trials. It is shown that the proposed models give some new unusual discrete models as well as the well-known continuous SRGMs. Through numerical examples with actual software failure data, two estimation methods for model parameters with grouped data are provided, and the predictive model performance is examined quantitatively.     

Problems with the estimation of stochastic differential equations using structural equations models

The present paper deals with the identification and maximum likelihood estimation of systems of linear stochastic differential equations using panel data. So we only have a sample of discrete observations over time of the relevant variables for each individual. A popular approach in the social sciences advocates the estimation of the “exact discrete model” after a reparameterization with LISREL or similar programs for structural equations models. The “exact discrete model” corresponds to the continuous time model in the sense that observations at equidistant points in time that are generated by the latter system also satisfy the former. In the LISREL approach the reparameterized discrete time model is estimated first without taking into account the nonlinear mapping from the continuous to the discrete time parameters. In a second step, using the inverse mapping, the fundamental system parameters of the continuous time system in which we are interested, are inferred. However, some severe problems arise with this “indirect approach”. First, an identification problem may arise in multiple equation systems, since the matrix exponential function denning some of the new parameters is in general not one‐to‐one, and hence the inverse mapping mentioned above does not exist. Second, usually some sort of approximation of the time paths of the exogenous variables is necessary before the structural parameters of the system can be estimated with discrete data. Two simple approximation methods are discussed. In both approximation methods the resulting new discrete time parameters are connected in a complicated way. So estimating the reparameterized discrete model by OLS without restrictions does not yield maximum likelihood estimates of the desired continuous time parameters as claimed by some authors. Third, a further limitation of estimating the reparameterized model with programs for structural equations models is that even simple restrictions on the original fundamental parameters of the continuous time system cannot be dealt with. This issue is also discussed in some detail. For these reasons the “indirect method” cannot be recommended. In many cases the approach leads to misleading inferences. We strongly advocate the direct estimation of the continuous time parameters. This approach is more involved, because the exact discrete model is nonlinear in the original parameters. A computer program by Hermann Singer that provides appropriate maximum likelihood estimates is described.     

Models for optimal harvest with convex function of growth rate of a population

Two models for growth of a population, which are described by a Cauchy problem for an ordinary differential equation with right-hand side depending on the population size and time, are investigated. The first model is time-discrete, i.e., the moments of harvest are fixed and discrete. The second model is time-continuous, i.e., a crop is harvested continuously in time. For autonomous systems, the second model is a particular case of the variational model for optimal control with constraints investigated in [1]. However, the prerequisites and the method of investigation are somewhat different, for they are based on Lemma1 presented below. In this paper, the existence and uniqueness theorem for the solution of the discrete and continuous problems of optimal harvest is proved, and the corresponding algorithms are presented. The results obtained are illustrated by a model for growth of the light-requiring green alge Chlorella. Bibliography: 6 titles. Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 77, 1993, pp. 75–86.     

Some contributions with Petri nets for the modelling, analysis and control of HDS

Petri nets (PN) are useful for the modelling, analysis and control of hybrid dynamical systems (HDS) because PN combine in a comprehensive way discrete events and continuous behaviours. On one hand, PN are suitable for modelling the discrete part of HDS and for providing a discrete abstraction of continuous behaviours. On the other hand, continuous PN are suitable for modelling the continuous part of HDS and for working out a continuous approximation of the discrete part in order to avoid the complexity associated with the exponential growth of discrete states. This paper focuses on the advantages of PN as a modelling tool for HDS. Investigations of such models for diagnosis and control issues are detailed.

Taking inspiration from the discrete event approach, sensor selection for diagnosis is discussed according to the structural analysis of the PN models. Faults are represented with fault transitions and a faulty behaviour occurs when a sequence of transitions is fired that contains at least one fault transition. Minimal sets of observable places are defined for detecting and isolating faulty behaviours.

Taking inspiration from the continuous time approach, flow control of HDS modelled with continuous PN is also investigated. Gradient-based controllers are introduced in order to adapt the firing speeds of some controllable transitions according to a desired trajectory of the marking. The equilibria and stability of the controlled system are studied with Lyapunov functions.     

Skew‐selfadjoint Dirac systems with rational rectangular Weyl functions: explicit solutions of direct and inverse problems and integrable wave equations

In this paper we study direct and inverse problems for discrete and continuous skew‐selfadjoint Dirac systems with rectangular (possibly non‐square) pseudo‐exponential potentials. For such a system the Weyl function is a strictly proper rational matrix function and any strictly proper rational matrix function appears in this way. In fact, extending earlier results, given a strictly proper rational matrix function we present an explicit procedure to recover the corresponding potential using techniques from mathematical system and control theory. We also introduce and study a nonlinear generalized discrete Heisenberg magnet model, extending earlier results for the isotropic case. A large part of the paper is devoted to the related discrete systems of which the pseudo‐exponential potential depends on an additional continuous time parameter. Our technique allows us to obtain explicit solutions for the generalized discrete Heisenberg magnet model and evolution of the Weyl functions.     

Modeling continuous levels of resistance to multidrug therapy in cancer

Multidrug resistance consists of a series of genetic and epigenetic alternations that involve multifactorial and complex processes, which are a challenge to successful cancer treatments. Accompanied by advances in biotechnology and high-dimensional data analysis techniques that are bringing in new opportunities in modeling biological systems with continuous phenotypic structured models, we investigate multidrug resistance by studying a cancer cell population model that considers a multi-dimensional continuous resistance trait to multiple drugs. We compare our continuous resistance trait model with classical models that assume a discrete resistance state and classify the cases when the continuum and discrete models yield different dynamical patterns in the emerging heterogeneity in response to drugs. We also compute the maximal fitness resistance trait for various continuum models and study the effect of epimutations. Finally, we demonstrate how our approach can be used to study tumor growth with respect to the turnover rate and the proliferating fraction. We show that a continuous resistance level model may result in different dynamics compared with the predictions of other discrete models.     

Online Surrogate Problem Methodology for Stochastic Discrete Resource Allocation Problems

We consider stochastic discrete optimization problems where the decision variables are nonnegative integers. We propose and analyze an online control scheme which transforms the problem into a surrogate continuous optimization problem and proceeds to solve the latter using standard gradient-based approaches, while simultaneously updating both the actual and surrogate system states. It is shown that the solution of the original problem is recovered as an element of the discrete state neighborhood of the optimal surrogate state. For the special case of separable cost functions, we show that this methodology becomes particularly efficient. Finally, convergence of the proposed algorithm is established under standard technical conditions; numerical results are included in the paper to illustrate the fast convergence of this approach.     

Inventory control as a discrete system control for the fixed-order quantity system

This paper shows how to model a problem to find optimal number of replenishments in the fixed-order quantity system as a basic problem of optimal control of the discrete system. The decision environment is deterministic and the time horizon is finite. A discrete system consists of the law of dynamics, control domain and performance criterion. It is primarily a simulation model of the inventory dynamics, but the performance criterion enables various order strategies to be compared. The dynamics of state variables depends on the inflow and outflow rates. This paper explicitly defines flow regulators for the four patterns of the inventory: discrete inflow – continuous/discrete outflow and continuous inflow – continuous/discrete outflow. It has been discussed how to use suggested model for variants of the fixed-order quantity system as the scenarios of the model. To find the optimal process, the simulation-based optimization is used.     

Discrete quantity approach to continuous simulation modelling

Traditionally, simulation executives have been divided into discrete-event and continuous-time executives. Some systems require modelling using both discrete and continuous parts. Hybrid simulation executives have the drawback that they treat discrete and continuous parts of a system in completely different ways. Here it is shown how continuous models may be simulated using a discrete executive: the novel discrete quantity approach (DQA). The method could also be used to allow a continuous part to be added to a discrete model without the need for a hybrid executive.