Robust Stability and Stabilization of Discrete Singular Systems with Interval Time-varying Delay and Linear Fractional Uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Delay-dependent robust control for uncertain discrete singular systems with time-varying delay

The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent robust stability condition is derived and expressed in terms of linear matrix inequalities (LMIs). A suitable robust state feedback control law is presented, which guarantees that the resultant closed-loop system is regular, causal and stable for all admissible uncertainties. Numerical examples are given to demonstrate the applicability of the proposed method.

Designing Discrete Predictor-Based Controllers for Networked Control Systems with Time-varying Delays:Application to A Visual Servo Inverted Pendulum System

A discrete predictor-based control method is developed for a class of linear time-invariant networked control systems with a sensor-to-controller time-varying delay and a controller-to-actuator uncertain constant delay,which can be potentially applied to vision-based control systems.The control scheme is composed of a state prediction and a discrete predictor-based controller.The state prediction is used to compensate for the effect of the sensor-to-controller delay,and the system can be stabilized by the discrete predictor-based controller.Moreover,it is shown that the control scheme is also robust with respect to slight message rejections.Finally,the main theoretical results are illustrated by simulation results and experimental results based on a networked visual servo inverted pendulum system.

Fault detection filter design for linear discrete time-varying systems with multiplicative noise

The problem of fault detection for linear discrete timevarying systems with multiplicative noise is dealt with.By using an observer-based robust fault detection filter（FDF） as a residual generator,the design of the FDF is formulated in the framework of H ∞ filtering for a class of stochastic time-varying systems.A sufficient condition for the existence of the FDF is derived in terms of a Riccati equation.The determination of the parameter matrices of the filter is converted into a quadratic optimization problem,and an analytical solution of the parameter matrices is obtained by solving the Riccati equation.Numerical examples are given to illustrate the effectiveness of the proposed method.

Scheme of optimal fault detection for linear discrete time-varying systems with delayed state

This paper deals with the problem of the optimal fault detection (FD) for linear discrete time-varying (LDTV) systems with delayed state and l(2)-norm bounded unknown input. The novelty lies in the designing of an evaluation function for the robust FD. The basic idea is to directly construct an evaluation function by using a weighted l(2)-norm of the measurement output, which achieves an optimal trade-off between the sensitivity to fault and the robustness to l(2)-norm bounded unknown input. To avoid complex computation, a feasible solution is obtained via the recursive computation by applying the orthogonal projection. It is shown that such an evaluation function provides a unified scheme for both the cases of unknown input being l(2)-norm bounded and jointly normal distribution, while a threshold may be chosen based on a priori knowledge of unknown input. A numerical example is given to demonstrate the effectiveness of the proposed method.

Improved Discrete Interval-Valued Stress-Strength Interference Model Based on Extended Universal Generating Function

In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.

Synchronization of stochastically hybrid coupled neural networks with coupling discrete and distributed time-varying delays

A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.

Reliability Bounds based on Universal Generating Function and Discrete Stress-strength Interference Model

A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress and strength, an interval statistics method is introduced. The processed results are formulated as two interval-valued random variables and are graphically represented component reliability are proposed based on the by using two histograms. The lower and upper bounds of universal generating function method and are calculated by solving two discrete stress-strength interference models. The graphical calculations of the proposed reliability bounds are presented through a numerical example and the confidence of the proposed reliability bounds is discussed to demonstrate the validity of the proposed method. It is showed that the proposed reliability bounds can undoubtedly bracket the real reliability value. The proposed method extends the exciting universal generating function method and can give an interval estimation of component reliability in the case of lake of sufficient experimental data. An application example is given to illustrate the proposed method

Real-Valued Discrete Gabor Transform of Linear Time-Varying Systems: Exact Representation and Approximation

An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existing algorithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm runs faster, can more easily be implemented in software or hardware, and leads to a more compact representation. Simulation results are given for demonstration.

Extensive numerical simulations on competitive growth between the Edwards–Wilkinson and Kardar–Parisi–Zhang universality classes

Extensive numerical simulations and scaling analysis are performed to investigate competitive growth between the linear and nonlinear stochastic dynamic growth systems, which belong to the Edwards–Wilkinson(EW) and Kardar–Parisi–Zhang(KPZ) universality classes, respectively. The linear growth systems include the EW equation and the model of random deposition with surface relaxation(RDSR), the nonlinear growth systems involve the KPZ equation and typical discrete models including ballistic deposition(BD), etching, and restricted solid on solid(RSOS). The scaling exponents are obtained in both the(1 + 1)-and(2 + 1)-dimensional competitive growth with the nonlinear growth probability p and the linear proportion 1-p. Our results show that, when p changes from 0 to 1, there exist non-trivial crossover effects from EW to KPZ universality classes based on different competitive growth rules. Furthermore, the growth rate and the porosity are also estimated within various linear and nonlinear growths of cooperation and competition.

Estimation of fracture size and azimuth in the universal elliptical disc model based on trace information

The geometric characteristics of fractures within a rock mass can be inferred by the data sampling from boreholes or exposed surfaces.Recently,the universal elliptical disc(UED)model was developed to represent natural fractures,where the fracture is assumed to be an elliptical disc and the fracture orientation,rotation angle,length of the long axis and ratio of short-long axis lengths are considered as variables.This paper aims to estimate the fracture size-and azimuth-related parameters in the UED model based on the trace information from sampling windows.The stereological relationship between the trace length,size-and azimuth-related parameters of the UED model was established,and the formulae of the mean value and standard deviation of trace length were proposed.The proposed formulae were validated via the Monte Carlo simulations with less than 5%of error rate between the calculated and true values.With respect to the estimation of the size-and azimuth-related parameters using the trace length,an optimization method was developed based on the pre-assumed size and azimuth distribution forms.A hypothetical case study was designed to illustrate and verify the parameter estimation method,where three combinations of the sampling windows were used to estimate the parameters,and the results showed that the estimated values could agree well with the true values.Furthermore,a hypothetical three-dimensional(3D)elliptical fracture network was constructed,and the circular disc,non-UED and UED models were used to represent it.The simulated trace information from different models was compared,and the results clearly illustrated the superiority of the proposed UED model over the existing circular disc and non-UED models。

基于离散烟花算法的通用弹药库存控制优化

近年来,随着我军实战化练兵水平的不断提高,对于后勤保障能力提升的要求更加迫切。但目前在通用弹药库存控制方面,难以满足目前高强度的训练需求,与实战化训练要求还有较大差距。论文针对目前存在的问题,构建三级库存控制模型,通过离散烟花算法进行求解,对于改善通用弹药的库存控制问题提出了新的思路。

A High-order Internal Model Based Iterative Learning Control Scheme for Discrete Linear Time-varying Systems

In this paper, an iterative learning control algorithm is proposed for discrete linear time-varying systems to track iterationvarying desired trajectories. A high-order internal model(HOIM) is utilized to describe the variation of desired trajectories in the iteration domain. In the sequel, the HOIM is incorporated into the design of learning gains. The learning convergence in the iteration axis can be guaranteed with rigorous proof. The simulation results with permanent magnet linear motors(PMLM) demonstrate that the proposed HOIM based approach yields good performance and achieves perfect tracking.

Pinning Synchronization of Discrete-Time Complex Networks with Different Time-Varying Delays

This paper investigates pinning synchronization of discrete-time complex networks with differen t time-varying delays.An important lemma is presen ted and proved,t hen detailed analysis is given to yield some synchronization criteria for this kind of net works.The results provide an effective way to synchronize discrete-time complex networks by reducing control cost.Furthermore,these theoretical results are illustrated by a complex network via two kinds of pinning schemes.Numerical simulations verify the feasibil计y of the proposed methods.

The Origin of Cosmic Structures Part 6: CMB Anisotropy

In a recent series of papers, we introduced a new model of nucleosynthesis in which the matter content of the universe came into existence at a time of about 4 × 10-5 s. At that time, a small percentage of the vacuum energy was converted into neutron/antineutron pairs with a very small excess of neutrons. This process was regulated by an imprint that was established in the vacuum during an initial Plank-era inflation. Immediately after their inception, annihilation and charge exchange reactions proceeded at a very high rate and ran to completion after an interval of about 10-11 s. By then, all the antibaryons had disappeared thereby establishing the matter/antimatter asymmetry of the universe. What remained were very high densities of mesons and leptons, somewhat lower densities of protons and neutrons, and finally, the very high density of photons that eventually became the CMB. The density of matter so created varied from one location to another in such a manner as to account for all cosmic structures and because the energy density of the photons varied in proportion to that of the matter, the CMB-to-be came into existence with an anisotropic spectrum already in place. For structures, the size of galaxy clusters, the initial anisotropy magnitudes were on the order of 25%. In this paper, we will follow the subsequent evolution of the photons and show that this model predicts with accuracy the temperature of the warmest anisotropies in the observed CMB spectrum. .

The Reality of Baryonic Acoustic Oscillations

The initial idea for baryonic acoustic oscillations (BAO) came about during early efforts to understand the origin of galaxies by studying perturbed versions of the Friedmann-Robertson-Walker (FRW) model. In more recent times, the emphasis has shifted to the idea that 2-point galaxy correlations embedded in the distribution of matter by the BAO could be used as a standard ruler to fix the parameters of cosmological models. In this paper, we first consider the actual business of extracting the correlation length from large data sets of measured galaxy locations. To facilitate this process, we introduce a much-improved method for extracting the correlation peak from the data set. Fundamental to this process in any model is the use of a fiducial cosmological model to transition from redshift space to comoving coordinate space where the correlations actually exist. The belief is that the correlation length so determined can then be reverted to redshift space to fix the parameters of cosmological models. We show, however, that this process is circular and hence of no value whatsoever for fixing model parameters. All one obtains are the parameters of the model used to transition to comoving space in the first place. Finally, we present simple arguments that show that the idea of BAO being responsible for the structure of the universe, i.e. the cosmic web, is unworkable.

职业本科计算机专业离散数学课教学改革初探

为了提升职业本科计算机类专业的教学水平,对其离散数学课的教学改革进行了探索,并给出了一套教学模式.该模式的核心是将离散数学课程内容与计算机专业知识融合起来教学.实践表明,该模式能有效提高职业本科学生学习的热情,以及学生的理论水平和实践能力.

Optimal LQG control for discrete time-varying system with multiplicative noise and multiple state delays

This paper is concerned with the optimal linear quadratic Gaussian(LQG)control problem for discrete time-varying system with multiplicative noise and multiple state delays.The main contributions are twofolds.First,in virtue of Pontryagin’s maximum principle,we solve the forward and backward stochastic difference equations(FBSDEs)and show the relationship between the state and the costate.Second,based on the solution to the FBSDEs and the coupled difference Riccati equations,the necessary and sufficient condition for the optimal problem is obtained.Meanwhile,an explicit analytical expression is given for the optimal LQG controller.Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.

应用型本科院校离散数学专创融合课程建设研究

离散数学是计算机专业理论性较强的基础课程,其理论方法研究的拓展在算法设计和解决复杂工程问题中发挥着至关重要作用。在高等教育改革和创新驱动发展战略的背景下,根据计算机专业人才培养方案,以培养学生思维、知识、能力和素养为目标,通过在教学目标上注重“双创”能力目标的培养、在教学内容上融入“双创”育人元素、在教学方法上引入创业项目驱动法、在课程考核方式上注重多元形成性评价、在教学团队上组建跨学科和跨学院融合队伍等措施开展离散数学专创融合课程建设,以促进计算机专业知识与“双创”训练的相互作用与相互关联,提升学生的创新思维能力、创新创业能力及算法设计的专业综合技能,提升课程教学质量。近年来,作者指导学生将离散数学知识应用于金融IC卡发卡系统、无线通信安全等研究领域,取得了良好的成效。

离散单元法评价煤层井壁稳定性

煤层属于裂缝发育的地层,钻井过程中井壁稳定性分析复杂,对煤层井壁稳定性进行评价十分必要。为此采用山西省沁水盆地樊庄3号煤层及取得的基本物理参数和节理参数,利用适合模拟节理煤层的离散元软件UDEC建立直井煤层模型,通过改变井底压力参数来分析井壁位移变化情况,得出了井眼模型宏观变化图像、微观位移矢量图以及8种不同状态下模型应力数据,并定量分析了8种状态下井眼附近离散单元失效情况。综合位移矢量图和定量分析结果,建立了井眼煤岩离散单元安全系数法,评价了煤层井壁在欠平衡条件下的井壁稳定性,评价结果认为:在该煤层参数下煤层井眼的最佳稳定井底压力区间值为4～7MPa。所建立的评价煤层井壁稳定性方法,可为煤层气气井钻井提供一种井壁分析分析手段。