Control Problem for a Piecewise Linear System with Uncertainties Based on Measurement Results

Differential Equations - We consider the problem of control of a piecewise linear system on a finite time horizon under uncertainty on the basis of incomplete and inaccurate information. A scheme...     

The Inviscid Initial Value Problem for a Piecewise Linear Mean Flow

The time evolution of a small disturbance on a piecewise linear mean flow, approximating a parabolic profile, is calculated using Fourier transform methods. The solution is found to consist of two parts: one dispersive, incorporating the spreading of waves; one convective, characterized by a convection of the disturbance with the local mean velocity. Two dispersive modes are found: one symmetric with respect to the channel center line and one antisymmetric. The dispersivity of the symmetric mode is in fair agreement with the symmetric mode obtained for inviscid parabolic flow, whereas the antisymmetric mode is misrepresented. One of the parts of the solution to the horizontal velocities is found to be purely three-dimensional. This results from fluid elements retaining part of their horizontal momentum as they are lifted up by the time integrated effect of the vertical velocity. Calculations of the development of a particular disturbance modeling two vortex pairs are also made. The results show that the dispersive part, although decaying, is largest for the vertical velocity. For the horizontal velocity the three-dimensional lift-up effect provides the largest amplitudes. This part does not show any sign of decay, in agreement with earlier analysis by Gustavsson [8] and Landahl [16]. This last effect partly explains the sensitivity to three-dimensional disturbances seen in transition experiments and calculations. Comparison of the solution to a full numerical simulation using the Navier-Stokes equations shows good agreement for short times.     

三角域上分片二次函数Bernstein多项式的退化性

设Ｓ_２（Ｔ）为三角域Ｔ的二阶剖分，本文给出在Ｓ_２（Ｔ）下分片二次函数f(P)∈Ｃ¹（Ｔ）的Ｂｅｒｎｓｔｃｉｎ多项式的退化性及递推公式。这里的条件Ｓ_２（Ｔ）及Ｃ¹（Ｔ）类都是重要的。我们举例说明更一般情况下分片二次函数Ｂｅｒｎｓｔｃｉｎ多项式的复杂性。     

Error Bounds of Constrained Quadratic Functions and Piecewise Affine Inequality Systems

We consider the error bounds for a piecewise affine inequality system and present a necessary and sufficient condition for this system to have an error bound, which generalizes the Hoffman result. Moreover, we study the error bounds of the system determined by a quadratic function and an abstract constraint.     

两个分段函数卷积的数值算法

本文推广了文［１］中卷积的数值计算方法，使之适用于更广的范围，并用Ｃ语言编程举例说明．     

Duality Bound Method for the General Quadratic Programming Problem with Quadratic Constraints

The purpose of this article is to develop a branch-and-bound algorithm using duality bounds for the general quadratically-constrained quadratic programming problem and having the following properties: (i) duality bounds are computed by solving ordinary linear programs; (ii) they are at least as good as the lower bounds obtained by solving relaxed problems, in which each nonconvex function is replaced by its convex envelope; (iii) standard convergence properties of branch-and-bound algorithms for nonconvex global optimization problems are guaranteed. Numerical results of preliminary computational experiments for the case of one quadratic constraint are reported.     

On a Boundary Value Problem for Pairs of Polyanalytic Functions

The necessary and sufficient conditions of Fredholmness and the index formula for a boundary value problems for a pair of polyanalytic functions, containing differential operators as well as operators with Carleman shift and conjugations, are obtained. Submitted: May 16, 2007. Accepted: November 5, 2007.     

Bifurcation of Limit Cycles for a Perturbed Piecewise Quadratic Differential Systems

In this paper, the bifurcation of limit cycles for planar piecewise smooth systems is studied which is separated by a straight line. We give a new form of Abelian integrals for piecewise smooth systems which is simpler than before. In application, for piecewise quadratic system the existence of 10 limit cycles and 12 small-amplitude limit cycles is proved respectively.     

A Projection Method for the Integer Quadratic Knapsack Problem

In this paper we present a new branch and bound algorithm for solving a class of integer quadratic knapsack problems. A previously published algorithm solves the continuous variable subproblems in the branch and bound tree by performing a binary search over the breakpoints of a piecewise linear equation resulting from the Kuhn-Tucker conditions. Here, we first present modifications to a projection method for solving the continuous subproblems. Then we implement the modified projection method in a branch and bound framework and report computational results indicating that the new branch and bound algorithm is superior to the earlier method.     

边值问题的变结构控制法

本文试图利用变结构控制方法来确保微分方程边值问题的解的唯一存在性,得到一些简明结果。此方法具有简单易行,可处理对象多样化,抗干扰性强的特点。     

Melnikov Functions for a Class of Piecewise Hamiltonian Systems

This paper is concerned with the number of limit cycles for a class of piecewise Hamiltonian systems with two zones separated by two semi-straight lines. By constructing a Poincar\''{e} map, we obtain explicit expressions of the first, second and third order Melnikov functions. In addition, we apply their expressions to give upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise polynomial Hamiltonian system.     

The Problem of the Pointwise Fourier Inversion for Piecewise Smooth Functions of Several Variables

We study the pointwise convergence problem for the inverse Fourier transform of piecewise smooth functions, i.e., whether S_rD f (\bx) ? f (\bx)S_{\rho D} f (\bx) \to f (\bx) as r? ￥\rho \to \infty . r? ￥\rho \to \infty . Here for \bx,\bxi ? \Rn\bx,\bxi \in \Rn S_rDf(\bmx)=\dsf1(2p)^n/2\intli_rD [^(f)](\bxi) e^{\dst iá\bmx,\bxi?} d\bxi . S_{\rho D}f(\bm{x})=\dsf1{(2\pi)^{n/2}}\intli_{\rho D} \widehat{f}(\bxi) e^{\dst i\langle\bm{x},\bxi\rangle} d\bxi~. is the partial sum operator using a convex and open set DD containing the origin, and rD={ r\bxi:\bxi ? D }\rho D=\left\{ \rho \bxi:\bxi\in D \right\}.     

Digital Stabilizer Design for a Switched Linear Control Delay System

The problem of designing a digital controller stabilizing a continuous-time switched linear control delay system is studied. The approach to stabilization successively includes the construction of a continuous-time–discrete-time closed-loop system with a digital controller, the transition to its discrete-time model, and the construction of a discrete-time controller by simultaneous stabilization methods.     

关于概率论中的分段函数问题

分段函数在概率论中有着广泛的应用.通过对几个概率问题的研究,探讨针对分段函数如何合理分段或分区域进行积分问题,体现分段函数在概率论中的重要性.     

Nonlinear Pressure Control of a Switched Hydraulic System

Hydraulic power transmission is often used in a variety of technical applications. Due to the nonlinear and often non smooth behaviour of some hydraulic components concerning their volume flow characteristics, the development of control strategies for hydraulic systems is challenging. Most developed control strategies base on linearized models, allowing only local operation in the environment of certain operating points. In this contribution, a nonlinear control strategy, based on the feedback linearization technique, allowing a global compensation of the nonlinearities [2], is developed for a minimal hydraulic circuit consisting of a pressure regulation valve, a vane pump and an ideal consumer. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

二次特征值问题中特征值和特征向量的可微性

二次特征值问题中特征值和特征向量的可微性,给出了其导数的计算公式及其算法.     

Piecewise Polynomial Approximate Solutions of an Automatic Control Problem

This paper considers piecewise polynomial approximate solutionsof a variational problem in which boundary conditions dependon values on the solution at interior points. The approximatesolutions are shown to converge to the solution of the variationalproblem in the L² and uniform norms, and algorithms for findingthe approximate solutions are obtained. Numerical examples arealso given.     

构造Birkhoff函数(组)的参数调节法

根据偏微分方程的Cauchy-Kovalevski可积性定理,将欠定的Birkhoff方程组转化为以Birkhoff函数组为未知变量的完备的偏微分方程组,提出了构造Birkhoff动力学函数的参数调节法．通过调节补偿方程中的两类可调的函数参数就能得到不同的Birkhoff函数组．并把构造Birkhoff函数组的参数调节法与Santilli构造方法进行了比较,例如研究了利用动力学系统独立的第一积分构造Birkhoff函数组的Hojman方法与参数调节法之间的关系．最后,给出应用实例验证了参数调节法的实用性及其与Santilli 3种构造方法的关系