Improved Adomian decomposition method (solving nonlinear non-homogenous initial value problem)

The Adomian decomposition method (ADM) cannot deal generally with the non-homogenous differential equations. The method still needs improvements. This paper introduces a qualitative improvement in the method. The improved method is called the improved Adomian decomposition method (IADM). A comparison between ADM and IADM shows that the ADM gives results that is not accepted in some examples and cannot solve the other examples while IADM solves the problems effectively and efficiently.     

精敏混合供应链解耦策略研究综述

精敏概念产出自20世纪末至今,十余年的历史,引起了国内外多位知名学者的高度关注。本文首先理顺了精敏混合供应链相关概念的研究现状和研究方法,将现有的方法归类为横向和纵向两大类,并主要分析了精敏混合供应链解耦策略和其方法模型,最后对精敏混合供应链解耦策略发展进行展望。     

An efficient method for solving Emden–Fowler equations

In this paper, He's variational iteration method (VIM) is applied to solve the Emden–Fowler type equations in the second-order ordinary differential equations (ODEs). In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The Lagrange multipliers in the functionals can be identified optimally via variational theory. This technique provides a sequence of functions which convergence to the exact solutions of the Emden–Fowler equations. Comparison with the exact solutions and the solutions by the Adomian decomposition method (ADM) show efficiency of VIM in solving equations with singularity.     

A hybrid approximation scheme for discretizing constrained quadratic optimal control problems

In this paper, a composite Chebyshev finite difference method for solving linear quadratic optimal control problems with inequality constraints on state and control variables is introduced. This method is an extension of Chebyshev finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well known Chebyshev–Gauss–Lobatto nodes. The excellent properties of hybrid functions are used to convert optimal control problem into a mathematical programming problem whose solution is much more easier than the original one. Various types of optimal control problems are investigated to demonstrate the effectiveness of the proposed approximation scheme. The method is simple, easy to implement and provides very accurate results.     

Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques

A general system of the time-dependent partial differential equations containing several arbitrary initial and boundary conditions is considered. A hybrid method based on artificial neural networks, minimization techniques and collocation methods is proposed to determine a related approximate solution in a closed analytical form. The optimal values for the corresponding adjustable parameters are calculated. An accurate approximate solution is obtained, that works well for interior and exterior points of the original domain. Numerical efficiency and accuracy of the hybrid method are investigated by two-test problems including an initial value and a boundary value problem for the two-dimensional biharmonic equation.     

Optimal control of linear delay systems via hybrid of block-pulse and Legendre polynomials

A method for finding the optimal control of a linear time varying delay system with quadratic performance index is discussed. The properties of the hybrid functions which consists of block-pulse functions plus Legendre polynomials are presented. The operational matrices of integration, delay and product are utilized to reduce the solution of optimal control to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.     

A matrix method for solving high-order linear difference equations with mixed argument using hybrid legendre and taylor polynomials

A numerical method for solving the higher order linear difference equations with variable coefficients and mixed argument under the mixed conditions is presented. The method is based on the hybrid Legendre and Taylor polynomials. The solution is obtained in terms of Legendre polynomials. IIIustrative examples are included to demonstrate the validity and applicability of the technique.     

Hybrid clustering for validation and improvement of subject-classification schemes

A hybrid text/citation-based method is used to cluster journals covered by the Web of Science database in the period 2002–2006. The objective is to use this clustering to validate and, if possible, to improve existing journal-based subject-classification schemes. Cross-citation links are determined on an item-by-paper procedure for individual papers assigned to the corresponding journal. Text mining for the textual component is based on the same principle; textual characteristics of individual papers are attributed to the journals in which they have been published. In a first step, the 22-field subject-classification scheme of the Essential Science Indicators (ESI) is evaluated and visualised. In a second step, the hybrid clustering method is applied to classify the about 8300 journals meeting the selection criteria concerning continuity, size and impact. The hybrid method proves superior to its two components when applied separately. The choice of 22 clusters also allows a direct field-to-cluster comparison, and we substantiate that the science areas resulting from cluster analysis form a more coherent structure than the “intellectual” reference scheme, the ESI subject scheme. Moreover, the textual component of the hybrid method allows labelling the clusters using cognitive characteristics, while the citation component allows visualising the cross-citation graph and determining representative journals suggested by the PageRank algorithm. Finally, the analysis of journal ‘migration’ allows the improvement of existing classification schemes on the basis of the concordance between fields and clusters.     

Stability analysis of almost periodic solutions of discontinuous BAM neural networks with hybrid time-varying delays and D operator

In the paper, we are concerned with a class of discontinuous BAM neural networks with hybrid time-varying delays and D operator. Based on the concept of Filippov solution, by means of the differential inclusions theory and the non-smooth analysis theory with Lyapunov-like approach, some new and novel sufficient conditions are derived to guarantee the existence, uniqueness and global exponential stability of almost-periodic solution of our proposed neural network model. To the authors’ knowledge, the results established in the paper are the only available results on the BAM neural networks, connecting the three main characteristics, i.e., discontinuous activation functions, hybrid time-varying delays and D operator. Some previous works in the literature are significantly extend and complement. Finally, two topical simulation examples are given to show the effectiveness of the established main results.     

混合聚类方法用于科学结构研究——以“心理学、社会学和教育学”领域为例

在前期的相关研究中,一种基于"引文-文本"相似度的混合聚类方法被用来对2002-2006年期间Webof Science数据库中8305种期刊进行了聚类分析,得到22聚类和7聚类两种体系。与之前的宏观分析不同,7聚类体系中的一个特定的聚类,即"心理学、社会学和教育学"聚类,将被集中研究。该聚类的内部学科结构以及其在22聚类体系中如何分解为三个子聚类将被细致地讨论和分析。对聚类之间的互引网络以及聚类中不同类型的"重要期刊"进行了展示,此外,还进一步将该聚类中760种期刊的混合聚类结果与Thomson-Reuters公司的ESI学科分类进行了对比,基于比较分析的结果,对该领域内部的科学结构进行了量化解读。     

改进智能水滴算法求解混合时间窗车辆路径问题

针对多目标车辆路径问题,研究了车载量、配送里程、混合时间窗等限制约束条件下,以最小配送费用和最少配送车辆数为目标建立多目标数学模型。在分析智能水滴算法求解类似离散问题时存在的局限性基础上,运用多种方式对其进行改进,并引入遗传算法选择、交叉及重组算子提高其性能,构建出两种改进智能水滴遗传混合算法,运用Solomon标准测试算例和实际算例进行验证。比较结果显示,改进后的混合算法能够有效解决离散问题,在持续寻优能力上较传统智能水滴算法和遗传算法更优；并且竞争选择改进智能水滴遗传混合算法求解算例效果最优。     

Finite-time convergent zeroing neural network for solving time-varying algebraic Riccati equations

Various forms of the algebraic Riccati equation (ARE) have been widely used to investigate the stability of nonlinear systems in the control field. In this paper, the time-varying ARE (TV-ARE) and linear time-varying (LTV) systems stabilization problems are investigated by employing the zeroing neural networks (ZNNs). In order to solve the TV-ARE problem, two models are developed, the ZNNTV-ARE model which follows the principles of the original ZNN method, and the FTZNNTV-ARE model which follows the finite-time ZNN (FTZNN) dynamical evolution. In addition, two hybrid ZNN models are proposed for the LTV systems stabilization, which combines the ZNNTV-ARE and FTZNNTV-ARE design rules. Note that instead of the infinite exponential convergence specific to the ZNNTV-ARE design, the structure of the proposed FTZNNTV-ARE dynamic is based on a new evolution formula which is able to converge to a theoretical solution in finite time. Furthermore, we are only interested in real symmetric solutions of TV-ARE, so the ZNNTV-ARE and FTZNNTV-ARE models are designed to produce such solutions. Numerical findings, one of which includes an application to LTV systems stabilization, confirm the effectiveness of the introduced dynamical evolutions.     

基于混合自适应的遗传工作流挖掘算法

针对遗传算法工作流挖掘容易过早收敛且局部寻优能力较差,导致得到的解不理想的情况,提出了一种基于混合遗传方法的工作流挖掘算法。该算法采用因果矩阵映射流程实例作为工作流模型的编码,在遗传算法的选择操作阶段采用锦标赛策略与精英保留策略相结合,在交叉变异阶段运用混合自适应方法,并结合模拟退火思想,使解的质量有了明显的提高。仿真实验表明,该算法与基于简单遗传方法的工作流挖掘算法相比效率更高。     

Dynamical behavior in a hybrid stochastic triple delayed prey predator bioeconomic system with Lévy jumps

In this paper, a hybrid triple delayed prey predator bioeconomic system with prey refuge and Lévy jumps is established, where both maturation delay for prey and predator population and gestation delay for predator population are considered. For deterministic system, positivity and uniform permanence of solution are discussed. Local stability of deterministic system around interior equilibrium is investigated due to variations of triple time delays. For stochastic system without time delay, sufficient conditions for stochastically ultimate boundedness and stochastic permanence are discussed. Existence of stochastic Hopf bifurcation and stochastic stability are investigated. For stochastic system with triple time delays, existence and uniqueness of global positive solution are studied. Finally, combined dynamic effects of triple time delays and Lévy jumps on the hybrid stochastic system are discussed by constructing appropriate Lyapunov functions. Numerical simulations are supported to illustrate theoretical analysis.     

A self-tuning hybrid active noise control system

Active Noise Control (ANC) systems are increasingly used to reduce environmental noises. A hybrid ANC system is a combination of feedforward and feedback structures in which the anti-noise signal is generated using both structures. Employing the advantages of feedforward and feedback structures enables a hybrid structure to have a high performance in controlling unwanted noise. The step size of filters used in ANC systems plays an essential role in its performance. Any variation from the appropriate value leads to divergence or inefficiency of the noise controller system. These parameters are often set experimentally, which is a time-consuming task. In addition, there is no guarantee that the system can adapt itself to situational changes. The objective of this paper is to propose a new self-tuning hybrid ANC method. Using this technique, the system continuously estimates the parameters during its operation. Results of computer simulations demonstrate the robustness of the proposed method.     

On the hybrid LQ-based control design for linear networked systems

This paper addresses a problem of optimal control design associated with the linear networked control systems (NCSs). We study a class of the conventional networked systems in the presence of time delays and propose a hybrid LQ-based theoretical and computational approach to the above NCSs. In particular, we develop an explicit theoretical representation of the networked control processes by an adequate auxiliary hybrid systems. For the constructive feedback control design procedure we derive the necessary hybrid Riccati-formalism and propose an implementable solution procedure.     

Stabilization of highly nonlinear hybrid systems driven by Lévy noise and delay feedback control based on discrete-time state observations

There are many hybrid stochastic differential equations (SDEs) in the real-world that don’t satisfy the linear growth condition (namely, SDEs are highly nonlinear), but they have highly nonlinear characteristics. Based on some existing results, the main difficulties here are to deal with those equations if they are driven by Lévy noise and delay terms, then to investigate their stability in this case. The present paper aims to show how to stabilize a given unstable nonlinear hybrid SDEs with Lévy noise by designing delay feedback controls in the both drift and diffusion parts of the given SDEs. The controllers are based on discrete-time state observations which are more realistic and make the cost less in practice. By using the Lyapunov functional method under a set of appropriate assumptions, stability results of the controlled hybrid SDEs are discussed in the sense of pth moment asymptotic stability and exponential stability. As an application, an illustrative example is provided to show the feasibility of our theorem. The results obtained in this paper can be considered as an extension of some conclusions in the stabilization theory.     

经验模态分解与均生函数-最优子集耦合模型在年径流预测中的应用

针对径流时间序列的非平稳特性及中长期预测精度低的问题,本文提出一种新的耦合预测方法：基于EMD分解的均生函数-最优子集回归（Mean Generating Function-Optimum Subset Regression,MGF-OSR）模型。首先利用经验模态分解（Empirical Mode Decomposition,EMD）方法对汾河上游上静游、汾河水库、寨上和兰村4座水文站的年径流序列进行平稳化处理,分别得到若干个固有模态函数（Intrinsic Mode Function,IMF）。对各阶固有模态函数分别建立MGF-OSR模型并进行预测,趋势项用直线拟合的方法进行预测,然后通过重构各预测值得到汾河上游4座水文站年径流量的预测结果,并与单独运用MGF-OSR模型的预测结果进行比较。结果表明,运用基于EMD分解的MGF-OSR模型对汾河上游4站年径流进行预测,准确率均为100%,确定性系数在0.975以上;而单一模型的预测准确率均为40%,确定性系数在0.732以下,耦合模型预测精度明显提高。     

The numerical solution of physical problems modeled as a systems of differential-algebraic equations (DAEs)

In this paper, the numerical solution of differential-algebraic equations is considered by Padé approximation method. We applied this method to an example which is a physical model problem. Firstly the physical model problem has been converted to power series, then the numerical solution of physical model problem was put into Padé series form. Thus we obtained numerical solution of physical model problem.     

Hybrid anti-bump control for switched nonlinear systems with event-triggering under sampled-data-based switching

This paper addresses the $H_{\infty }$ hybrid anti-bump control for switched nonlinear systems with event-triggering via the interval type-2 (IT2) fuzzy model. A unified framework of anti-bump performance for switched nonlinear systems called hybrid anti-bump performance is established to attenuate sudden big hybrid bumps caused by both triggering and switching. Then, we design a sampled-data-based switching strategy, under which we only need to check the switching conditions at discrete sampling instants. By using the multiple Lyapunov–Krasovskii functional theory and the constructed switching law, sufficient conditions are made for the considered systems to be asymptotically stable with both $H_{\infty }$ performance and hybrid anti-bump performance. Moreover, the switching law, the event-triggered scheme, and the event-triggered controllers are jointly designed. Finally, an electro-hydraulic model is exploited to verify the applicability and effectiveness of our method.