一类控制量非负的新型脉冲随机控制模型

提出并研究了一类新型的脉冲随机控制模型,其状态结构由关于半鞅的线性随机微分方程所确定,其控制费用函数为关于控制前状态与控制量的二元函数且其控制量保持非负.首先建立了一类新型的变分方程并证明了其解的存在性.通过对变分方程的解函数进行一系列随机分析处理,证明了最佳控制的存在性且对其结构进行了深入分析.此外,由于本文模型与以往文献中的随机控制模型有着重大差异,因而在分析手法上与以往文献相比颇多差异之处.可以预期,本文不仅在随机控制的研究中将具有重要的理论意义,而且在金融控制及证券管理方面也将有着广泛的应用价值.     

Arbitrary decay rate for two connected strings with joint anti-damping by boundary output feedback

In this paper, we are concerned with the boundary stabilization of two connected strings with middle joint anti-damping for which all eigenvalues of the (control) free system are located on the right complex plane. We first design an explicit state feedback controller to achieve exponential stability for the closed-loop system. Consequently, we design the output feedback by using infinite-dimensional observer. The backstepping approach is adopted in investigation. It is shown that by using one boundary stabilizer only, the output feedback can make the closed-loop system exponentially stable with arbitrary decay rate.     

A note on the differential regulator equation for non-minimum phase linear systems with time-varying exosystems

Some control problems in practice are often formulated as a linear output regulation problem with time-varying exosystems. Although this problem has been studied recently, an explicit and constructive solution has been given only for minimum phase systems. This paper presents a solution for non-minimum phase systems whose zero dynamics is hyperbolic (or has an exponentially dichotomic split in the case of time-varying zero dynamics). The idea is inspired by the non-causal stable inversion.     

A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients

We propose a compact split-step finite difference method to solve the nonlinear Schrödinger equations with constant and variable coefficients. This method improves the accuracy of split-step finite difference method by introducing a compact scheme for discretization of space variable while this improvement does not reduce the stability range and does not increase the computational cost. This method also preserves some conservation laws. Numerical tests are presented to confirm the theoretical results for the new numerical method by using the cubic nonlinear Schrödinger equation with constant and variable coefficients and Gross-Pitaevskii equation.     

A relativistic extension of the complex scaling method using oscillator basis functions

We develop the complex scaling method within the relativistic framework by expanding the Dirac spinors in the complete set of eigensolutions of a harmonic oscillator potential, and present the theoretical formalism of describing the discrete bound and resonant states on the same footing. Based on a well established and frequently used model, we demonstrate the utility and applicability of the extended method and examine the stability of the results with respect to the variations of the parameters of the model. Satisfactory agreements are found for all the calculated results in comparison with some other calculations in references. Especially, the present calculation in the nonrelativistic limit gives a consistent result with that in the nonrelativistic calculation.     

Numerical solution of Riccati equation using the cubic B-spline scaling functions and Chebyshev cardinal functions

Two numerical techniques are presented for solving the solution of Riccati differential equation. These methods use the cubic B-spline scaling functions and Chebyshev cardinal functions. The methods consist of expanding the required approximate solution as the elements of cubic B-spline scaling function or Chebyshev cardinal functions. Using the operational matrix of derivative, we reduce the problem to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the new techniques. The methods are easy to implement and produce very accurate results.     

Adaptive synchronization of uncertain coupled stochastic complex networks

In this paper, the problem of adaptive synchronization of uncertain coupled complex networks is investigated. Some controllers and adaptive laws are designed to ensure achieving synchronization of a general complex network model. In particular, synchronization of coupled stochastic networks subject to random perturbations is studied, with a referenced node introduced as the target node for synchronization. An example is simulated on delayed neural networks coupled in a small‐world network topology, which demonstrates the feasibility and effectiveness of the proposed adaptive control method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Multi-relaxation-time lattice Boltzmann model for axisymmetric flows

In this paper, a lattice-Boltzmann equation (LBE) with multi relaxation times (MRT) is presented for axisymmetric flows. The model is an extension of a recent model with single-relaxation-time [Guo et al., Phys. Rev. E 79, 046708 (2009)], which was developed based on the axisymmetric Boltzmann equation. Due to the use of the MRT collision model, the present model can achieve better numerical stability. The model is validated by some numerical tests including the Hagen-Poiseuille flow, the pulsatile Womersley flow, and the external flow over a sphere. Numerical results are in excellent agreement with analytical solutions or other available data, and the improvement in numerical stability is also confirmed.     

基于矩形NAM和偏微分方程的灰度图像压缩方法

借助矩形NAM图像表示方法和偏微分方程技术,提出一种新的灰度图像压缩方法.该方法在编码端把原始图像逆布局为若干矩形子块,并采用坐标压缩方法存储每个子块的位置、大小.在解码端,采用偏微分方程进行图像修复,有效消除解码图像中的方块效应.该方法的时间复杂度为 ,其中n为灰度图像像素数.实验表明:在保持图像质量的前提下,该方法具有更高的压缩比和更少的块数,具有较高实用价值.     

基于流场的爆炸分裂效果模拟

通过分析冲击波气流的运动特点,对Navier-Stokes方程进行合理简化。根据简化后的方程所反映出的气流速度变化规律,提出描述冲击波气流运动的扩散模型。基于该模型所定义的流场,对碎片的运动进行控制,实现对冲击波作用下物体碎片飞散效果的模拟。实验结果表明,该方法具有较强的真实感,能够满足实时性要求。