具有学习机制的离散差分演化算法

如何将差分演化算法应用于离散领域是目前该领域的一个热点研究问题。用分布佑计算法对搜索空间中优质解的分布进行建模,然后根据建立的模型抽样产生新解,利用分布佑计这种全局信息学习的机制,提出具有学习机制的离散差分演化算法并用于求解多维背包问题。实验结果表明,提出的算法具有良好的性能。     

Approaches to Robust Filtering Design of Discrete Time Fuzzy Dynamic Systems

This paper presents two filter design methods for discrete time fuzzy dynamic systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting filtering error system is globally stable with guaranteed H_infin or generalized H₂ performance and the filter gains can be obtained by solving a set of linear matrix inequalities. Two simulation examples are also given to illustrate the performance of the proposed approaches.     

An Invariance Principle for Nonlinear Discrete Autonomous Dynamical Systems

This note proposes an extension of LaSalle's invariance principle for nonlinear discrete autonomous dynamical systems. The invariance principle is extended to allow the first difference of the auxiliar scalar function (usually a Lyapunov function) to be positive in some bounded regions. Moreover, a uniform version is proposed to deal with nonlinear discrete dynamical systems that vary with parameters. Both extensions have the original invariance principle as a particular case. As a consequence, a larger class of systems can be treated with this new theory. The extensions are very useful to obtain attractor estimates as well as their corresponding stability regions. The uniform version, in particular, is useful to obtain estimates that are uniform regarding parameters     

Periodic solutions of a single species discrete population model with periodic harvest/stock

We discuss a discrete population model describing single species growth with periodic harvest/stock. The theory of coincidence degree is applied to show that the model equation admits two periodic solutions. Under minor technical assumptions, we show that one of these two periodic solutions is positive and attracts almost all positive solutions.     

基于离散度与拉伸技术的粒子群优化算法

采用离散度作为衡量种群多样性的指标.在粒子群初始化阶段,种群的离散度必须满足一定的要求才能开始迭代;在算法迭代过程中,惯性权重、加速系数的调整都与当前粒子群的离散度相关;当种群的离散度小于一定数值时,进行保优重初始化,适应度函数拉伸操作,重新迭代.由于算法在初始化阶段依据离散度进行了限定,要求粒子尽量平均分布,算法运行...     

Quantitative Characterizations of Exponential Convergence Property of Nonlinear Discrete Dynamical Systems

In this technical note, we consider the exponential convergence property of the trajectories of nonlinear discrete dynamical systems with exponential stability. Based on an invariant quantity derived from Lyapunov functions of the systems, the essential and quantitative relationship between exponential convergence property of trajectories and the Lyapunov functions is revealed.     

Intelligent Control Paradigm for Dynamic Discrete Event System Simulation

Simulation based control of discrete event systems has been a potential approach to support decision-making in the manufacturing scenario. In this paper, a knowledge intensive simulation modelling approach for a discrete even system is investigated. Based on the proposed simulation model, a robust control mechanism is presented that is believed to add significant value to discrete event dynamic system. The algorithm utilises neural network feedforward control plus robust proportional derivative feedback control to achieve control performance and output stability. The novel simulation approach, as well as the proposed controller, is implemented in an Extend TM environment and the effectiveness and usefulness of the proposed controller are verified, industrially, in the hard disk drive assembly process, a significant component of the Singapore manufacturing economy.     

A note on “A multiple-vendor single-buyer integrated inventory model with a variable number of vendors”

In this technical note, an alternative solution procedure to the model that Glock (2011) developed is presented. In particular, we take into account the same assumptions, but the total cost function is reformulated, i.e., the step-type discontinuity is replaced by a logistic approximation and the total costs of the system are computed on the whole set of preselected suppliers. Subsequently, we show that the total cost function possesses some properties in terms of convexity and continuity that allow the exploitation of standard constrained nonlinear minimization algorithms. Finally, tests conducted on the same set of problems that Glock (2011) originally considered illustrate the good performances of the solution procedure developed in this note.     

Hierarchical Fuzzy Systems for Function Approximation on Discrete Input Spaces With Application

This paper investigates the capabilities of hierarchical fuzzy systems to approximate functions on discrete input spaces. First, it is shown that any function on a discrete space has an arbitrary separable hierarchical structure and can be naturally approximated by hierarchical fuzzy systems. As a by-product of this result, a discrete version of Kolmogorov's theorem is obtained; second, it is proven that any function on a discrete space can be approximated to any degree of accuracy by hierarchical fuzzy systems with any desired separable hierarchical structure. That is, functions on discrete spaces can be approximated more simply and flexibly than those on continuous spaces; third, a hierarchical fuzzy system identification method is proposed in which human knowledge and numerical data are combined for system construction and identification. Finally, the proposed method is applied to the market condition performance modeling problem in site selection decision support and shows the better performance in both accuracy and interpretability than the regression and neural network approaches. In additions, the reason and mechanism why hierarchical fuzzy systems outperform regression and neural networks in this type of application are analyzed.      

An Asymptotically Exact Approach to Robust Semidefinite Programming Problems with Function Variables

This technical note provides an approximate approach to a semidefinite programming problem with a parameter-dependent constraint and a function variable. This problem covers a variety of control problems including a robust stability/performance analysis with a parameter-dependent Lyapunov function. In the proposed approach, the original problem is approximated by a standard semidefinite programming problem through two steps: first, the function variable is approximated by a finite-dimensional variable; second, the parameter-dependent constraint is approximated by a finite number of parameter-independent constraints. Both steps produce approximation error. On the sum of these approximation errors, this technical note provides an upper bound. This bound enables quantitative analysis of the approach and gives an efficient way to reduction of the approximation error. Moreover, this technical note discusses how to verify that an optimal solution of the approximate problem is actually optimal also for the original problem.      

Discrete thickness optimization via piecewise constraint penalization

Structural engineers are often constrained by cost or manufacturing considerations to select member thicknesses from a discrete set of values. Conventional, gradient-free techniques to solve these discrete problems cannot handle large problem sizes, while discrete material optimization (DMO) techniques may encounter difficulties, especially for bending-dominated problems. To resolve these issues, we propose an efficient gradient-based technique to obtain engineering solutions to the discrete thickness selection problem. The proposed technique uses a series of constraints to enforce an effective stiffness-to-mass and strength-to-mass penalty on intermediate designs. In conjunction with these constraints, we apply an exact penalty function which drives the solution towards a discrete design. We utilize a continuation approach to obtain approximate solutions to the discrete thickness selection problem by solving a sequence of relaxed continuous problems with increasing penalization. We also show how this approach can be applied to combined discrete thickness selection and topology optimization design problems. To demonstrate the effectiveness of the proposed technique, we present both compliance and stress-constrained results for in-plane and bending-dominated problems.     

离散时间Petri网的模糊模型

离散时间Petri网是一种系统模拟和分析的有效工具，它可以结合图形和分析描述评估离散事件系统的动态执行．基于T—S模糊模型，提出用于描述离散时间Petri网的模糊模型，讨论该模型适应于TtPNs的情况，用以推广文章结论，并且给出用于TtPNs的线性模糊控制规则．同时，文章还给出TtPNs聚合的结论．     

Discrete linear Hamiltonian eigenvalue problems

This paper introduces general discrete linear Hamiltonian eigenvalue problems and characterizes the eigenvalues. Assumptions are given, among them the new notion of strict controllability of a discrete system, that imply isolatedness and lower boundedness of the eigenvalues. Due to the quite general assumptions, discrete Sturm-Liouville eigenvalue problems of higher order are included in the presented theory.     

Static Output Feedback Control Synthesis for Linear Systems With Time-Invariant Parametric Uncertainties

This technical note is concerned with the problem of designing robust static output feedback controllers for linear discrete and continuous-time systems with time-invariant polytopic uncertainties. Sufficient conditions for static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities. Furthermore, the results are also extended to H₂ static output feedback controller designs. Numerical examples are given to illustrate the effectiveness of the proposed design methods.     

离散自由搜索算法

针对离散组合优化问题,给出一个自由搜索的算法。但是仅仅通过自由搜索算法求得的解,往往存在交叉现象,针对这个问题提出将离散自由搜索算法和交叉消除相结合的算法,这样不仅大大地提高了自由搜索算法运算过程的收敛速度,而且较大程度地提升了结果的质量。利用旅行商问题(TSP)标准库中的测试数据对所提算法进行了验证,结果表明该算法比遗传算法性能提高了约1.6%。     

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.     

卫星通信天线伺服系统的离散滑模控制算法研究

船载卫星天线易受干扰而导致跟踪精度和通信质量下降。为改善天线系统的性能,实现了基于DSP的天线伺服控制器,在设计的天线伺服系统中应用基于指数趋近率的离散滑模变结构控制算法,并且进行了设计分析和实验仿真。实验结果表明,基于此算法,较容易设计满足系统稳定性的离散控制器。与传统的PID算法相比,该算法具有较好的实时适应性,伺服系统对连续或突加干扰的敏感度大大下降,鲁棒性明显增强。     

基于LabVIEW的离散频谱校正技术仿真

在许多工程应用领域,离散频谱分析发挥着越来越重要的作用,频谱分析结果的精确程度是在工程应用取得成功的关键因素之一,但是在现阶段,经过快速傅里叶变换得到的离散频谱,其频率、幅值和相位均可能产生较大误差.基于这一原因,研究了离散频谱的校正技术,通过LabVIEW软件编写出两种基于频谱校正方法(比值校正法和能量重心校正法)的校正程序,并构造相应的函数仿真来验证该方法的可行性.通过仿真结果分析,表明该程序可以进行离散频谱校正,大大提高频谱分析的精度,取得了不错的效果.     

Alignment Properties in Ordinal Comparison of Discrete Event Dynamic Systems

In the design and optimization of discrete event dynamic systems, it is often necessary to order alternative designs based on their relative performance, i.e., to rank them from best to worst. In this paper, alignment of observed performance orders with true orders is considered and properties of the alignment are investigated. Spearman's rank correlation coefficient is a measure of agreement between the observed performance orders and the true ones. It is shown that Spearman's coefficient converges exponentially in the simulation time or observation time, which gives a strong evidence of the efficiency of order comparison for discrete event dynamic systems. In the context of simulation, the effect of simulation dependence on the alignment is also discussed. It is found that neither independent simulation nor the scheme of common random numbers (CRN), a popular scheme for variance reduction, can yield dominant performance. Finally, numerical examples based on a networking optimization problem are provided to illustrate the convergence of Spearman's coefficient. In these examples, the standard clock (SC) simulation technique provides much faster convergence than either independent simulations or CRN simulations. Both the SC and CRN methods use the same random number sequence to drive many events in parallel; however, under SC the events driving the parallel experiments are all identical, whereas under CRN they may be different.     

Performance Analysis of Gradient Neural Network Exploited for Online Time-Varying Matrix Inversion

This technical note presents theoretical analysis and simulation results on the performance of a classic gradient neural network (GNN), which was designed originally for constant matrix inversion but is now exploited for time-varying matrix inversion. Compared to the constant matrix-inversion case, the gradient neural network inverting a time-varying matrix could only approximately approach its time-varying theoretical inverse, instead of converging exactly. In other words, the steady-state error between the GNN solution and the theoretical/exact inverse does not vanish to zero. In this technical note, the upper bound of such an error is estimated firstly. The global exponential convergence rate is then analyzed for such a Hopfield-type neural network when approaching the bound error. Computer-simulation results finally substantiate the performance analysis of this gradient neural network exploited to invert online time-varying matrices.