Recursive approximate solution to time-varying matrix differential Riccati equation: linear and nonlinear systems

An approximate solution is proposed for linear-time-varying (LTV) systems based on Taylor series expansion in a recursive manner. The intention is to present a fast numerical solution with reduced sampling time in computation. The proposed procedure is implemented on finite-horizon linear and nonlinear optimal control problem. Backward integration (BI) is a well known method to give a solution to finite-horizon optimal control problem. The BI performs a two-round solution: first one elicits an optimal gain and the second one completes the answer. It is very important to finish the backward solution promptly lest in practical work, system should not wait for any action. The proposed recursive solution was applied for mathematical examples as well as a manipulator as a representative of complex nonlinear systems, since path planning is a critical subject solved by optimal control in robotics.     

基于WTFMC算法的递归模糊神经网络结构设计

针对递归模糊神经网络(Recurrent fuzzy neural network, RFNN)的递归量难以自适应的问题, 提出一种基于小波变换–模糊马尔科夫链(Wavelet transform fuzzy Markov chain, WTFMC)算法的RFNN模型.首先, 在时间维度上记录隐含层神经元的模糊隶属度, 并采用小波变换将该时间序列进行分解, 通过模糊马尔科夫链对子序列的未来时段进行预测, 之后将各预测量合并后代入递归函数中得到具有自适应性的递归量.其次, 利用梯度下降算法更新RFNN的参数来保证神经网络的精度.最后, 通过非线性系统建模中几个基准问题和实际污水处理中关键水质参数的预测实验, 证明了该神经网络模型的可行性和有效性.     

Differential evolution-based nonlinear system modeling using a bilinear series model

This paper presents a new modeling method for nonlinear dynamic systems based on using bilinear series model. Basically, bilinear model is an extension of infinite impulse response (IIR) filter and belongs to the recursive nonlinear system model, i.e., its past output signals will heavily affect the present output. This kind of model can efficiently approximate a large class of nonlinear systems with fewer parameters than other non-recursive models. To adjust the model kernels, we here adopt an evolutionary computation called the differential evolution (DE) algorithm. This algorithm is based on real-valued manipulations and has a good convergence property for finding the global solution or the near global solution of optimized problem. Design steps of DE-based nonlinear system modeling are clearly given in this study. Finally, two kinds of digital systems are illustrated to demonstrate the efficiency of the proposed method.     

具有广义正则化与遗忘机制的在线贯序超限学习机

针对非平稳时间序列预测问题,提出一种具有广义正则化与遗忘机制的在线贯序超限学习机算法.该算法以增量学习新样本的方式实现在线学习,以遗忘旧的失效样本的方式增强对非平稳系统的动态跟踪能力,并通过引入一种广义的$l_2$正则化使其具有持续的正则化功能,从而保证算法的持续稳定性.仿真实例表明,所提出算法具有较同类算法更好的稳定性和更小的预测误差,适用于具有动态变化特性的非平稳时间序列在线建模与预测.     

A novel solution for maze traversal problems using artificial neural networks

In this paper we have addressed the problem of finding a path through a maze of a given size. The traditional ways of finding a path through a maze employ recursive algorithms in which unwanted or non-paths are eliminated in a recursive manner. Neural networks with their parallel and distributed nature of processing seem to provide a natural solution to this problem. We present a biologically inspired solution using a two level hierarchical neural network for the mapping of the maze as also the generation of the path if it exists. For a maze of size S the amount of time it takes would be a function of S (O(S)) and a shortest path (if more than one path exists) could be found in around S cycles where each cycle involves all the neurons doing their processing in a parallel manner. The solution presented in this paper finds all valid paths and a simple technique for finding the shortest path amongst them is also given. The results are very encouraging and more applications of the network setup used in this report are currently being investigated. These include synthetic modeling of biological neural mechanisms, traversal of decision trees, modeling of associative neural networks (as in relating visual and auditory stimuli of a given phenomenon) and surgical micro-robot trajectory planning and execution.     

近似非齐次无偏GM(1,1) 模型的递推解法及应用

针对传统近似非齐次灰建模可能出现参数复数解的问题, 提出无偏灰色GM(1,1) 模型的递推解法, 从而减少由差分方程向微分方程跳跃而导致误差的问题. 给出不同初始条件下非齐次无偏GM(1,1) 模型的递推预测公式,并在此基础上, 将递推公式运用于时间序列分段, 提出基于近似非齐次无偏GM(1,1) 模型的时间序列分段表示方法. 实例结果表明, 所提出的递推模型能够获得较高的拟合精度, 分析结果验证了基于灰色预测模型在时间序列分段表示中的有效性和实用性.

     

Fast evolving neuro-fuzzy model and its application in online classification and time series prediction

A strategy for improving speed of the previously proposed evolving neuro-fuzzy model (ENFM) is presented in this paper to make it more appropriate for online applications. By considering a recursive extension of Gath?CGeva clustering, the ENFM takes advantage of elliptical clusters for defining validity region of its neurons which leads to better modeling with less number of neurons. But this necessitates the computing of reverse and determinant of the covariance matrices which are time consuming in online applications with large number of input variables. In this paper a strategy for recursive estimation of singular value decomposition components of covariance matrices is proposed which converts the burdensome computations to calculating reverse and determinant of a diagonal matrix while keeping the advantages of elliptical clusters. The proposed method is applied to online detection of epileptic seizures in addition to prediction of Mackey?CGlass time series and modeling a time varying heat exchanger. Simulation results show that required time for training and test of fast ENFM is far less than its basic model. Moreover its modeling ability is similar to the ENFM which is superior to other online modeling approaches.     

定向判别分析新算法及其在沉积化学中的应用

介绍了处理多元有序数据的定向判别分析新方法原理、建模流程、应用流程及其在沉积化学中的应用实例。这种判别分析将分类建模与判别归类分开,求解与专业知识结合。新方法用多组或逐步判别分析对多元有序数据建模,应用时根据应用领域的知识对样本归属作初步定向,然后选择模型的相关局部进行判别归类,从而实现有序判别。这种方法用于解决由于时间序列多元数据周期性造成的样本分类颠倒问题。在塔里木盆地沉积岩时间序列化学数据的应用实例中,解决了石油井下地层预测和归类问题。     

递归思想在指派问题中的运用

提出将矩阵进一步缩小的方法来求指派问题的解,用匈牙利解法求指派问题的解,然后用递归思想求解指派问题,并对两种方法的优缺点进行比较.通过对比可以知道,两种方法所得的结果是一样的.匈牙利算法的优点是算法时问复杂度较小,缺点是解题过程比较复杂.递归思想的优点是解题过程比较简单,缺点是算法时间复杂度较大.     

用VB编写Hanoi塔问题动态演示程序

递归技术是算法设计过程中的一个重要技术,Hanoi塔问题是一个典型的适合用递归技术求解的问题。将Hanoi塔问题的递归执行过程利用编程方法动态演示出来,有助于人们结合Hanoi塔问题加深对递归技术的理解。     

非平稳时序数据的分段辨识及其递推算法

在实际生活中,广泛地存在着一类在整体上属于非平稳但又可转化为数段局部平稳的时序数据,对该类非平稳时序数据的辨识问题进行了研究,并提出了一种具有递推机制的分段辨识算法.该算法从平稳时序数据的定义出发,以均值、方差及自相关函数等数字统计特征为校验统计量,构造了具有递推机制的均值突变点、方差突变点及自相关函数突变点的析出算法,在此基础上,从被辨识的非平稳序列中划分出数段局部平稳的子序列,进一步,应用Burg算法对各局部平稳子序列进行了自回归的递推辨识.实验表明,新设计的算法能以较小的位置偏差析出各局部平稳子序列的分界点,同时,在保证较高精度的辨识条件下,计算效能获得了显著的提升.     

A comparison between neural-network forecasting techniques-casestudy: river flow forecasting

Estimating the flows of rivers can have significant economic impact, as this can help in agricultural water management and in protection from water shortages and possible flood damage. The first goal of the paper is to apply neural networks to the problem of forecasting the flow of the River Nile in Egypt. The second goal of the paper is to utilize time series as a benchmark to compare between several neural-network forecasting methods. We compare four different methods to preprocess the inputs and outputs, including a novel method proposed here based on discrete Fourier series. We also compare three different methods for the multistep ahead forecast problem: the direct method, the recursive method, and the recursive method trained using a backpropagation through time scheme. We also include a theoretical comparison between these three methods. The final comparison is between different methods to perform a longer horizon forecast, and that includes ways to partition the problem into several subproblems of forecasting K steps ahead.     

Decision-directed multivariate empirical bayes classification with nonstationary priors

A decision-directed learning strategy is presented to recursively estimate (i.e., track) the time-varying a priori distribution for a multivariate empirical Bayes adaptive classification rule. The problem is formulated by modeling the prior distribution as a finite-state vector Markov chain and using past decisions to estimate the time evolution of the state of this chain. The solution is obtained by implementing an exact recursive nonlinear estimator for the rate vector of a multivariate discrete-time point process representing the decisions. This estimator obtains the Doob decomposition of the decision process with respect to the a-field generated by all past decisions and corresponds to the nonlinear least squares estimate of the prior distribution. Monte Carlo simulation results are provided to assess the performance of the estimator.     

Josephus问题分析与探讨

Josephus问题是一个经典的递归问题。本文从问题的编程解决入手，提出静态数组、环链表、递归等3种解题方案。本文还对问题作进一步分析，考虑解的稳定点,最后提出一个优化方案，将问题的解决归约到一个较小的规模。     

A non-iterative shooting method for a non-linear diffusion problem using automatic differentiation

We present a non-iterative shooting method for the solution of a non-linear two-point boundary value problem that models the steady-state temperature distribution in a cylinder of unit radius. By non-iterative it is meant that there is no need to solve one or more initial value problems repeatedly. The method of this article avoids the need for such repetition by numerically obtaining a single algebraic non-linear equation involving only the initial condition. Thus, the appropriate initial condition for the final solution is available just after one solution of the initial value problem corresponding to an arbitrary initial value. In addition, the solution of the initial value problem is obtained as a Taylor series expansion of arbitrary order, using a technique known as automatic differentiation, which is the process of obtaining the coefficients in the Taylor series expansion using recursive formulas. Thus, the method does not face the need to deal with step size issues or the need to carry out lengthy algebraic manipulations. The method successfully reproduces the solutions obtained previously by other researchers.     

光网络中波长通道优化路由算法研究

通过对波长通道路由问题具体特点的数学分析,将问题分解为多个小规模的线性数学规划模型,设计了一个基于当前解邻域变换的快速搜索算法。模拟试验表明,同启发式算法相比,该算法能在较短的时间内取得更好的优化效果。     

A recursive method for solving unconstrained tangentialinterpolation problems

An efficient recursive solution is presented for the one-sided unconstrained tangential interpolation problem. The method relies on the triangular factorization of a certain structured matrix that is implicitly defined by the interpolation data. The recursive procedure admits a physical interpretation in terms of discretized transmission lines. In this framework the generating system is constructed as a cascade of first-order sections. Singular steps occur only when the input data is contradictory, i.e., only when the interpolation problem does not have a solution. Various pivoting schemes can be used to improve numerical accuracy or to impose additional constraints on the interpolants. The algorithm also provides coprime factorizations for all rational interpolants and can be used to solve polynomial interpolation problems such as the general Hermite matrix interpolation problem. A recursive method is proposed to compute a column-reduced generating system that can be used to solve the minimal tangential interpolation problem     

An analysis of program execution on a recursive stream-oriented data flow architecture

The functional or applicative approach to the development of software leads to the natural exposure of parallelism. Data flow architectures are designed to exploit this parallelism. This paper describes a method for modeling and analyzing program execution on a stream-oriented, recursive data flow architecture. Based on a maximum path length technique, a recursive analysis of nodes (corresponding to high level constructs) results in an approximation of the time required to execute the program given adequate resources. By relating the structure of a program to the degree of exhibited parallelism, this method provides a useful tool for studying parallelism and evaluating certain problem classes to be run on similar architecutures.     

Estimation of object motion parameters from noisy images

An approach is presented for the estimation of object motion parameters based on a sequence of noisy images. The problem considered is that of a rigid body undergoing unknown rotational and translational motion. The measurement data consists of a sequence of noisy image coordinates of two or more object correspondence points. By modeling the object dynamics as a function of time, estimates of the model parameters (including motion parameters) can be extracted from the data using recursive and/or batch techniques. This permits a desired degree of smoothing to be achieved through the use of an arbitrarily large number of images. Some assumptions regarding object structure are presently made. Results are presented for a recursive estimation procedure: the case considered here is that of a sequence of one dimensional images of a two dimensional object. Thus, the object moves in one transverse dimension, and in depth, preserving the fundamental ambiguity of the central projection image model (loss of depth information). An iterated extended Kalman filter is used for the recursive solution. Noise levels of 5-10 percent of the object image size are used. Approximate Cramer-Rao lower bounds are derived for the model parameter estimates as a function of object trajectory and noise level. This approach may be of use in situations where it is difficult to resolve large numbers of object match points, but relatively long sequences of images (10 to 20 or more) are available.