一种利用切比雪夫逼近求解库存最优控制的方法

针对供应链中库存随着需求的变化可能导致的积压和对生产,或采购,产生的不利影响,为更好地协调生产,或采购,并减少产品库存$研究了一类基于库存约束和动态时变需求下的多品种,多周期,多循环的生产与库存的最优控制模型.结合最优控制理论,给出一种采用切比雪夫多项式逼近和高斯-切比雪夫数值积分对库存最优控制问题进行数值求解的方法.实例分析表明该方法是可行的.

     

时变需求下生产与库存系统的最优控制决策方法

针对供应链中库存随着需求的变化可能导致的积压和对生产(或采购)产生的不利影响,为了更好地协调生产(或采购)并减少产品库存,本文研究了以生产为中心的一类基于库存约束和动态线性时变需求下的多品种、多周期、多循环的生产与库存的最优控制模型,结合应用最优控制理论,给出了一种采用切比雪夫多项式逼近和高斯.切比雪夫数值积分对最优控制问题进行数值求解的方法.最后,对某一时变需求情况下的模型应用MATLAB软件进行了求解,得到了生产(采购)与库存的最优控制策略,有效地保证了供应链系统的持续稳定的循环.     

改进切比雪夫意义下最佳逼近方法与应用

切比雪夫意义下的最佳逼近方法具有广泛用途。但若按逼近的相对误差加以改进、则逼近结果会有更大的实际意义。本文针对一般工程应用,给出了三次以下的解析结果和使用实例。     

基于双曲切比雪夫逼近的光谱模板构造

我国正在实施的大型巡天项目(LAMOST),迫切需要一套恒星光谱自动识别与分类系统.恒星光谱的自动识别与分类很大程度上依赖于恒星光谱模板库的质量.恒星光谱分类模板库中模板光谱数量越少,恒星光谱的自动处理速度越快.论文给出了一种基于切比雪夫双曲线逼近(two curve Chebyshev approximation)分...     

预测型切比雪夫多项式

预测型切比雪夫多项式,是切比雪夫多项式及最佳逼近理论在预测中的一个推广应用,可以解决一般预测中预测的可知、可控性问题。文中通过讨论后指出,在预测中,当预测误差不超过已知最大绝对误差时,预测将成为可知;当预测区间不超过已知最大范围时,预测将成为可控。基于这个原理,建立了一种具有预测功能的预测型切比雪夫多项式,[Gn(x)]多项式。论证了该多项式依据的微分方程、相关定义、有关性质、数学表式;阐述了该多项式的存在性;给出了[Gn(x)]多项式在[y(x)≠0]条件下构成的预测型最佳逼近[g(x)]多项式;提供了[g(x)]多项式得以实现的具体算法;介绍了一种使预测结果更接近实际值的误差补偿法;并给出了若干应用实例。     

切比雪夫逼近的深度神经网络并行加速

深度神经网络(Deep Neural Network,DNN)中数据量巨大,且卷积层计算复杂度高,使得其难以在资源有限的嵌入式GPU上进行部署,因此需要对其进行并行加速设计.本文提出采用切比雪夫多项式对卷积核进行逼近,并将该优化方案应用在面向图像重构的DNN中以实现卷积操作的并行化处理,降低计算复杂度.然后为优化后的网...     

切比雪夫等波纹逼近低通滤波器在MSP430单片机中的实现

以切比雪夫等波纹逼近理论为基础,设计了切比雪夫等波纹逼近FIR低通滤波器。在 以MSP430F133单片机为核心的可燃性气体检测报警系统中,采用该低通滤波器,对可燃性气体浓 度信号处理,获得较好的效果。     

切比雪夫等波纹逼近滤波器在可燃气体浓度信号仿真中的应用

以切比雪夫等波纹逼近滤波器为理论基础,对MSP430F133单片机现场采集的可燃气体浓度信号进行滤波仿真。来阐述切比雪夫等波纹逼近低通滤波器的设计方法以及滤波器参数的优化,进而说明切比雪夫等波纹逼近滤波器的优越性能。     

切比雪夫多项式及其插值法在检测中的应用研究

介绍了切比雪夫多项式及其插值算法的实现，结合传感器输出特性的非线性补偿、非线性校正以及检测系统中的复杂计算，分别给出了应用实例。结果表明，这些方法能用于智能传感器系统以及嵌入式微控制器中的软件数据处理，提高检测的实时性和精度，在工程上具有很好的应用价值。     

利用切比雪夫不等式的背景建模算法

针对运动目标检测问题中的背景建模问题,提出一种结合切比雪夫不等式和核密度估计的背景建模方法.首先利用样本均值与样本方差及切比雪夫不等式,快速计算各像素点属于前景和背景的概率,判别出前景点、背景点及可疑点.对可疑点再利用核密度估计方法,估计其属于前景与背景的概率密度来进行背景前景判别,最后通过设定阈值完成实时背景建模.实验结果证明,利用切比雪夫不等式能快速区分有明显特征的前景点与背景点,采用背景更新算法能得到理想的背景图像,降低了背景图像提取的误差,显著地提高了背景建模的速度.     

Multi-product multi-chance-constraint stochastic inventory control problem with dynamic demand and partial back-ordering: A harmony search algorithm

In this paper, a multiproduct inventory control problem is considered in which the periods between two replenishments of the products are assumed independent random variables, and increasing and decreasing functions are assumed to model the dynamic demands of each product. Furthermore, the quantities of the orders are assumed integer-type, space and budget are constraints, the service-level is a chance-constraint, and that the partial back-ordering policy is taken into account for the shortages. The costs of the problem are holding, purchasing, and shortage. We show the model of this problem is an integer nonlinear programming type and to solve it, a harmony search approach is used. At the end, three numerical examples of different sizes are given to demonstrate the applicability of the proposed methodology in real world inventory control problems, to validate the results obtained, and to compare its performances with the ones of both a genetic and a particle swarm optimization algorithms.     

Pseudospectral methods for solving infinite-horizon optimal control problems

An important aspect of numerically approximating the solution of an infinite-horizon optimal control problem is the manner in which the horizon is treated. Generally, an infinite-horizon optimal control problem is approximated with a finite-horizon problem. In such cases, regardless of the finite duration of the approximation, the final time lies an infinite duration from the actual horizon at t=+∞. In this paper we describe two new direct pseudospectral methods using Legendre–Gauss (LG) and Legendre–Gauss–Radau (LGR) collocation for solving infinite-horizon optimal control problems numerically. A smooth, strictly monotonic transformation is used to map the infinite time domain t∈[0,∞) onto a half-open interval τ∈[−1,1). The resulting problem on the finite interval is transcribed to a nonlinear programming problem using collocation. The proposed methods yield approximations to the state and the costate on the entire horizon, including approximations at t=+∞. These pseudospectral methods can be written equivalently in either a differential or an implicit integral form. In numerical experiments, the discrete solution exhibits exponential convergence as a function of the number of collocation points. It is shown that the map ?:[−1,+1)→[0,+∞) can be tuned to improve the quality of the discrete approximation.     

Minimizing control variation in nonlinear optimal control

In any real system, changing the control signal from one value to another will usually cause wear and tear on the system’s actuators. Thus, when designing a control law, it is important to consider not just predicted system performance, but also the cost associated with changing the control action. This latter cost is almost always ignored in the optimal control literature. In this paper, we consider a class of optimal control problems in which the variation of the control signal is explicitly penalized in the cost function. We develop an effective computational method, based on the control parameterization approach and a novel transformation procedure, for solving this class of optimal control problems. We then apply our method to three example problems in fisheries, train control, and chemical engineering.     

A computational method for solving optimal control and parameter estimation of linear systems using Haar wavelets

In this article, a computational method based on Haar wavelet in time-domain for solving the problem of optimal control of the linear time invariant systems for any finite time interval is proposed. Haar wavelet integral operational matrix and the properties of Kronecker product are utilized to find the approximated optimal trajectory and optimal control law of the linear systems with respect to a quadratic cost function by solving only the linear algebraic equations. It is shown that parameter estimation of linear system can be done easily using the idea proposed. On the basis of Haar function properties, the results of the article, which include the time information, are illustrated in two examples.     

Dynamic programming and viscosity solutions for the optimal control of quantum spin systems

The purpose of this paper is to describe the application of the notion of viscosity solutions to solve the Hamilton-Jacobi-Bellman (HJB) equation associated with an important class of optimal control problems for quantum spin systems. The HJB equation that arises in the control problems of interest is a first-order nonlinear partial differential equation defined on a Lie group. Hence we employ recent extensions of the theory of viscosity solutions to Riemannian manifolds in order to interpret possibly non-differentiable solutions to this equation. Results from differential topology on the triangulation of manifolds are then used develop a finite difference approximation method for numerically computing the solution to such problems. The convergence of these approximations is proven using viscosity solution methods. In order to illustrate the techniques developed, these methods are applied to an example problem.     

An efficient algorithm for optimal control of PWA systems with polyhedral performance indices

We present an algorithm for the computation of explicit optimal control laws for piecewise affine (PWA) systems with polyhedral performance indices. The algorithm is based on dynamic programming (DP) and represents an extension of ideas initially proposed in Kerrigan and Mayne [(2003). Optimal control of constrained, piecewise affine systems with bounded disturbances. In Proceedings of the 41st IEEE conference on decision and control, Las Vegas, Nevada, USA, December], and Baoti? et al. [(2003). A new algorithm for constrained finite time optimal control of hybrid systems with a linear performance index. In Proceedings of European control conference, Cambridge, UK, September]. Specifically, we show how to exploit the underlying geometric structure of the optimization problem in order to significantly improve the efficiency of the off-line computations. An extensive case study is provided, which clearly indicates that the algorithm proposed in this paper may be preferable to other schemes published in the literature.     

Applying a finite-horizon numerical optimization method to a periodic optimal control problem

Computing a numerical solution to a periodic optimal control problem can be difficult, especially when the period is unknown. A method of approximating a solution to a stochastic optimal control problem using Markov chains was developed in [Krawczyk, J. B. (2001). A Markovian approximated solution to a portfolio management problem. Information Technology for Economics and Management, 1, http://www.item.woiz.polsl.pl/issue/journal1.htm]. This paper describes the application of that method to a periodic optimal control problem formulated in [Gaitsgory, V. & Rossomakhine, S. (2006). Linear programming approach to deterministic long run average problems of optimal control. SIAM Journal on Control and Optimization, 44(6), 2006-2037]. As a result, approximately optimal feedback rules are computed that can control the system both on and off the optimal orbit.     

An ecologically inspired direct search method for solving optimal control problems with Bézier parameterization

An optimal control problem can be formulated through a set of differential equations describing the trajectory of the control variables that minimize the cost functional (related to both state and control variables). Direct solution methods for optimal control problems treat them from the perspective of global optimization: i.e. perform a global search for the control function that optimizes the required objective. In this article we use a recently developed ecologically inspired optimization technique called Invasive Weed Optimization (IWO) for solving such optimal control problems. Usually the direct solution method operates on discrete n-dimensional vectors and not on continuous functions. Consequently it can become computationally expensive for large values of n. Thus, a parameterization technique is required to represent the control functions using a small number of real-valued parameters. Typically, direct methods based on evolutionary computing techniques parameterize control functions with a piecewise constant approximation. This has obvious limitations both for accuracy in representing arbitrary functions, and for optimization efficiency. In this paper a new parameterization is introduced using Bézier curves, which can accurately represent continuous control functions with only a few parameters. It is combined with IWO into a new evolutionary direct method for optimal control. The effectiveness of the new method is demonstrated by solving a wide variety of optimal control problems.