有关混沌及其控制与同步的一些理解

从实例出发，对非线性耗散系统中的混沌及其控制与同步研究中遇到的有关基本概念和问题作一些哲理性解释。内容涉及混沌的基本假设及其标志性特征、通向混沌的道路、混沌系统的相空间基本格局、混沌控制的基本策略、所谓‘混沌同步’以及‘噪声诱导同步’的实质含意、随机混沌的约定性定义、以及数值仿真在混沌研究中的作用等。对混沌及其控制与同步、以及随机混沌提出了一些独特的新见解。     

基于T-S模糊模型的Lorenz超混沌系统和Zhou超混沌系统广义同步

本文研究了两类新超混沌系统的广义渐近同步问题,首先建立Lorenz超混沌系统和Zhou超混沌系统精确的T-S模糊模型,然后基于线性系统理论和并行分布补偿技术,设计模糊状态反馈控制器,将模糊同步误差系统渐近镇定在零点,实现Lorenz超混沌系统和Zhou超混沌系统的广义渐近同步。最后通过仿真验证广义同步方法的有效性。     

混沌同步控制策略构造方法研究

水下辐射噪声中的低频线谱是影响潜艇声隐身性能的主要因素,线谱混沌化控制技术通过处于混沌状态的非线性隔振系统将低频线谱转换为宽频混沌谱,可以实现频谱重构并降低线谱强度。前期研究表明,利用广义混沌同步方法可以实现变工况下隔振系统的持续混沌化,在某些情况下还能显著减小振幅,为线谱混沌化控制理论提供了新思路。然而,目前要利用广义混沌同步产生小振幅的持续混沌运动,只能通过"试错"来选择合适的混沌同步控制策略,还没有形成系统的方法。为此,提出了一种混沌同步控制策略构造方法。结合耦合Duffing隔振系统对该构造方法进行验证和说明,并将该方法应用于两自由度非线性隔振系统。     

基于有限时间函数投影的电力系统混沌控制

电力系统作为复杂的非线性系统,其混沌振荡会表现为随机的、突发性的或情节严重的机电振荡,会伴随着非周期现象出现,将导致电力系统大区域和大面积的停电事故,严重威胁电网的安全稳定运行。为了有效地抑制电力系统的混沌行为,并充分考虑控制方法在实际工程中的应用价值,基于有限时间理论和函数投影同步理论,提出了一种有限时间函数投影同步控制的电力系统混沌控制方法。该方法借鉴混沌同步思想,通过将混沌电力系统与理想状态电力系统在有限时间内实现完全同步,间接地实现电力系统的混沌控制。推导了稳定性定理的数学证明,并进行了相应的数值模拟来验证该方法在电力系统混沌控制中的有效性。理论及仿真结果表明,该方法可以有效地使混沌电力系统在有限时间内实现稳定控制,且对外部干扰具有强鲁棒性。     

新混沌系统分析及其同步控制

提出了一个新混沌系统,通过Matlab对该系统进行了分岔图、Lyapunov指数、相图等仿真分析,证实了在选定特定参数下,该系统为混沌系统。随着参数的改变,该系统会出现周期--倍周期--混沌--周期--倍周期--混沌交替现象,具有较复杂的动力学特性及对初值的敏感性,通过Multisim电路仿真证实了该系统的物理可实现性。针对提出的新混沌系统,设计了错位投影同步控制器,从理论上证实了在同步控制器的作用下该系统与Chen混沌系统达到了同步,通过Matlab仿真证实了同步控制器的有效性。最后,在同步控制器作用下实现了新混沌系统和Chen混沌系统的数字加密传输。     

纳米系统的反控制片时混沌

通过设计由经典混沌映射所表示的按时驱动能够实现纳米系统的片时混沌。本文应用子动力学理论相应给出了演化算子一般性的谱分解,然后给出了应用一维混沌映射驱动原始系统进入片时混沌的步骤。给出了量子点系统表现反控制和同步片时混沌的相应的计算。     

基于自适应控制策略下的Rossler和Chen混沌系统的同步

讨论了2个著名的混沌系统的混沌同步控制问题．在响应系统与驱动系统具有相同的结构，但未知驱动系统参数的情况下，设计出了有效的自适应控制器，实现了系统间的全局状态同步．仿真结果验证了该控制器的有效性．     

分数阶具有不确定项和外扰的超混沌金融系统的滑模同步

本文利用滑模控制与比例积分滑模控制技巧研究了分数阶具有不确定项和外扰的一类超混沌金融系统的同步问题,运用分数阶微积分设计出滑模函数,通过设计适应规则构造出适应控制器,得到了分数阶不确定超混沌金融系统取得滑模同步和积分滑模同步的两个充分性条件．Matlab 数值仿真验证了理论结果．文中滑模函数的设计、控制器的构造及适应规则的选取对研究整数阶超混沌金融系统的滑模同步具有可移植性,所使用的方法为研究分数阶混沌系统提供了思路,同时分数阶系统的相关结果可以移植到整数阶系统的同步问题．     

两自由度非线性隔振系统线谱混沌化控制技术研究

线谱混沌化是提高潜艇声隐身性能的主要手段,但难以实现小振幅下的持续混沌化;同时,非线性隔振系统由于多个吸引子共存,混沌化品质依赖于初始条件和系统参数。为此,利用开环加非线性闭环方法研究两自由度非线性隔振系统的吸引子迁移和线谱混沌化。建立两自由度非线性隔振系统的动力学方程并分析其全局性态,得到系统的全局分岔特性及吸引子共存规律;通过开环加非线性闭环方法实现不同吸引子之间的迁移控制,使系统在不同初始条件下始终运行于基础振动最小的混沌吸引子上;利用开环加非线性闭环耦合方法实现驱动系统和响应系统之间的广义混沌同步,使系统在不同参数下始终处于小振幅持续混沌运动。仿真结果表明该方法具有可行性和稳定性,能实现隐匿线谱信息和保持隔振性能的双重功能。     

一类超混沌系统的参数辨识和混沌反同步

设计一种参数观测器,对一类不确定超系统中的未知参数进行识别,接着对该系统的混沌反同步进行研究,以李雅普诺夫稳定性理论为基础,设计合适的非线性控制器,仿真结果表明,在参数观测器和控制器的共同作用下,参数未知超混沌系统实现混沌反同步,从而证明该观测器和控制器的有效性。     

Reminiscence of a teacher and a researcher

Abstract

The names of previous after-dinner speakers at this conference read like a Who is Who of Quantum Optics and Photonics research. When the organizers of this conference asked me to present an after-dinner talk I felt honored by the invitation, but also humbled by joining such a distinguished company. This fact gives me a “Leitmotiv” for my present talk, because being humbled by, and feeling inferior to, all the brilliant minds one encounters in one's career is a necessary occurrence, which most of the younger listeners in this audience have either experienced or will experience. I have witnessed these feelings as advisor to students at MIT. Many of them fear that everything worth doing has already been done. There is a simple answer to this. Do not get discouraged, work harder and you will also make a respectable contribution to science or engineering.     

Ceramesh — a company and a membrane

Claimed as a major advance in microfiltration technology, Ceramesh is an inorganic composite ceramic membrane that can be produced in a flat sheet suitable for use in process-scale crossflow filtration systems. The membrane combines a metal mesh and a ceramic to give strength, formability and both chemical and heat resistance The Ceramesh membrane technology has its origins in work carried out at Alcan Separations in Banbury and has been under development since 1988. Some of the original team had also worked on the development of the Anopore membrane, since commercialised by Anotec, and these close personal links have been maintained. Ceramesh Ltd was formed in 1990 by Alcan and a venture capital company with the aim of speeding the development of the membrane and ensuring its early introduction to the commercial filtration market. These objectives have now been achieved and by the middle of 1992 the Ceramesh membrane has been evaluated for a number of specific applications, been incorporated into a range of commercial filtration equipment, and formally launched into the chemical-process industries at the Eurochem exhibition held in Birmingham in June.     

Separation and slip between a layer and a substrate caused by a tensile load

The paper treats the elastic layer that is pressed uniformly against a half space and is subsequently subjected to a concentrated force tending to induce slip and separation between the bodies. The formulation, based on known results for discrete dislocations, reduces the problem to a coupled system of integral equations which is solved numerically. Various results of interest are given graphically.     

Aberrations from a prism and a grating

Formulas for the wave aberrations introduced into a beam by a prism or a plane grating are derived from the theory of plane symmetric systems. Emphasis is made on the field-dependent aberrations.     

Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate

We derive what we believe to be new analytical relations to describe the Fraunhofer diffraction of the finite-radius plane wave by a helical axicon (HA) and a spiral phase plate (SPP). The solutions are deduced in the form of a series of the Bessel functions for the HA and a finite sum of the Bessel functions for the SPP. The solution for the HA changes to that for the SPP if the axicon parameter is set equal to zero. We also derive what we believe to be new analytical relations to describe the Fresnel and Fraunhofer diffraction of the Gaussian beam by a HA are derived. The solutions are deduced in the form of a series of the hypergeometric functions. We have fabricated by photolithography a binary diffractive optical element (a HA with number n=10) able to produce in the focal plane of a spherical lens an optical vortex, which was then used to perform rotation of several polystyrene beads of diameter 5 microm.     

Stress analysis of a strip with a step and a crack

Stress analysis for a strip of which widths are different at the right and left handsides is carried out for before and after occurrence of a crack at a corner of a step. The strip is analyzed as a thin plate bending problem subject to transverse bending and torsion, and as a plane eleastic problem subject to bending in the plane and uniaxial tension. The rational mapping function of a sum of fractional expressions and complex variable method are used. Stress distribution and stress intensity factors are obtained.     

Interaction between a liquid and a cylindrical body touching a wall

An exact solution is obtained for the problem of interaction between the ideal liquid homogeneously moving at infinity and streamlining a round cylinder touching a solid wall.     

The interaction between a dislocation and a crack

The solution is given in closed form to the problem. of the elastic field round a dislocatiop ,and a,; crack in any relative position when the field is independent of one of the three cartesian co-ordinates,, The, analysis holds for the most general anisotropy.

---

Zusammenfassung Die Lösung wird dem Problem des elastischen Feldes rund um eine Verschiebung und einen Riss in irgendeiner relativen Stellung in geschlossener Form gegeben, wenn das Feld von den drei kartesischen Koordinaten unabhängig ist. Die Analyse gilt fiir die generalste Anisotropie.

---

Résumé Le pròbleme du champ de tension élastique autour d' une dislocation et d' une fissure en positions relatives quelconques est résolu sous une forme générale dans le cas d' une champ élastique indépendant d' une des trois coordonnees cartésiennes.L' analyse effectuée couvre le cas de 1' anisotropie la plus générale.

     

MHD flow and heat transfer in a channel bounded by a shrinking sheet and a plate with a porous substrate

This research is concerned with heat transfer and an MHD flow of a viscous incompressible electrically conducting fluid in a channel bounded by a shrinking sheet and an impermeable plate. A fluid-saturated porous substrate of a very low permeability is attached to the impermeable plate. The flow in the channel is induced by the upper shrinking sheet, where a constant suction is imposed. By introducing the similarity transformations, the governing partial differential equations for the flow and heat transfer are transformed to ordinary differential equations which are solved analytically by using the perturbation series method for a small shrinking parameter. Expressions for the velocity distribution, temperature field, skin friction, and heat transfer rate are obtained, and numerical computations are carried out for various parameters. The results are displayed graphically and discussed.