Optimal bounded control of first-passage failure of quasi-integrable Hamiltonian systems with wide-band random excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged It$\ddot{\rm o}$ equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

Optimal bounded control of first-passage failure of strongly non-linear oscillators under combined harmonic and white-noise excitations

A procedure for designing the optimal bounded control of strongly non-linear oscillators under combined harmonic and white-noise excitations for minimizing their first-passage failure is proposed. First, a stochastic averaging method for strongly non-linear oscillators under combined harmonic and white-noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equations and their boundary and final time conditions for the control problems of maximizing reliability and of maximizing mean first-passage time are formulated from the averaged Ito equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraint. Finally, the conditional reliability function, the conditional probability density and mean of the first-passage time of the optimally controlled system are obtained from solving the backward Kolmogorov equation and Pontryagin equation. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation. (C) 2003 Elsevier Ltd. All rights reserved.

Numerical Solution for Polymer Transient Flows in a Circle Bounded Composite Formation

A new numerical model for transient flows of polymer solution in a circular bounded composite formation is presented in this paper. Typical curves of the wellbore transient pressure are yielded by FEM. The effects of non-Newtonian power-law index, mobility and boundary distance have been considered. It is found that for the mobility ratio larger than 1, which is favorable for the polymer flooding, the pressure derivative curve in log-log form rises up without any hollow. On the other hand, if the pressure derivative curve has a hollow and then is raised up, we say that the polymer flooding fails. Finally, the new model has been extended to more complicated boundary case.

Stabilization of Uncertain Nonholonomic Dynamic Systems with Bounded Inputs

The sliding mode approach and the multi-step control strategy are exploited to propose a stabilizing controller for uncertain nonholonomic dynamic systems with bounded inputs. This controller can stabilize the system to an arbitrarily small neighborhood about its equilibrium in a finite time .Its application to a nonholonomic wheeled mobile robot is described. Simulation result shows that the proposed controller is effective

Influence Of Free Surface Curvature Of A Liquid Layer On The Critical Marangoni Convection

The Pearson instability was suggested to discuss the onset of Marangoni convection in a liquid layer of large Prandtl number under an applied temperature difference perpendicular to the free surface in the microgravity environment. In this case, the temperature distribution on the curved free surface is nonuniform, and the thermocapillary convection is induced and coupled with the Marangoni convection. In the present paper the effect of volume ratio of the liquid layer on the critical Marangoni convection and the corresponding spatial variation of the convection structure in zero-gravity condition were numerically investigated by two-dimensional model. (C) 2008 Elsevier Ltd. All rights reserved.

The annular crack in a nonhomogeneous matrix surrounding a fiber under torsional loading .2. The crack going through the bimaterial interface into the fiber

The axisymmetric problem of an elastic fiber perfectly bonded to a nonhomogeneous elastic matrix which contains an annular crack going through the interface into the fiber under axially symmetric shear stress is considered. The nature of the stress singularity is studied. It is shown that at the irregular point on the interface, whether the shear modulus is continuous or discontinuous the stresses are bounded. The problem is formulated in terms of a singular integral equation and can be solved by a regular method. The stress intensity factors and crack surface displacement are given.

Few-cycle relativistic solitons in plasmas

A set of exact one-dimensional solutions to coupled nonlinear equations describing the propagation of a relativistic ultrashort circularly polarized laser pulse in a cold collisionless and bounded plasma where electrons have an initial velocity in the laser propagating direction is presented. The solutions investigated here are in the form of quickly moving envelop solitons at a propagation velocity comparable to the light speed. The features of solitons in both underdense and overdense plasmas with electrons having different given initial velocities in the laser propagating direction are described. It is found that the amplitude of solitons is larger and soliton width shorter in plasmas where electrons have a larger initial velocity. In overdense plasmas, soliton duration is shorter, the amplitude higher than that in underdense plasmas where electrons have the same initial velocity.

透镜自重变形引起波像差的有限元分析

在用大口径、长焦距平行光管模拟激光远场特性时，其光组透镜在重力作用下的变形不能忽略，为了分析对出射光束质量的影响，采用有限元分析软件“ANSYS”建立了平行光管光组中声400mm平凸透镜的有限元模型，给出一种分析透镜轴向变形引起的波像差的方法，在不同工况下，计算了平凸透镜在重力作用下轴向变形的峰谷值和均方根值，对轴向变形量均方根值最小工况画出了透镜表面变形的等值线图，计算了声350mm通光口径内的波像差峰谷值和均方根值，对平行光管光组的波像差做出估计，验证了设计的合理性。

Structural and optical properties of InAs/In0.52Al0.48As self-assembled quantum wires on InP(001)

Six-stacked InAs/In0.52Al0.48As self-assembled quantum wires (QWRs) on InP(001) by molecular-beam epitaxy (MBE) have been studied by high-resolution transmission electron microscopy (HRTEM) and polarized PL measurements. We obtained the chemical lattice fringe (CLF) image of InAs self-assembled QWRs embedded in the In0.52Al0.48As matrix by the interference between the (002)-diffracted beam and the transmitted beam in the image plane of the objective lens. The results show that the InAs QWRs were bounded by (113), (001) and (114) facets. Both the size and strain distribution in QWRs were determined. It was found that with the growth of successive periods, the height and height fluctuation of InAs QWRs decreased from the bottom period to the upper one. Some suggestions are put forward for further improving the uniformity of the stacked InAs QWRs. (c) 2005 Elsevier B.V. All rights reserved.

Structure approximate based on double weighted neural network

Double weighted neural network; is a kind of new general used neural network, which, compared with BP and RBF network, may approximate the training samples with a move complicated geometric figure and possesses a even greater approximation. capability. we study structure approximate based on double weighted neural network and prove its rationality.

限界模型检测方法及其应用

形式化验证主要是通过精确的分析来证明或证伪硬件或软件系统中一些明确的声明或者性质。形式化验证方法在广义上可以分成两大类：模型检测和定理证明。模型检测由对模型的所有状态和迁移做详尽访问的自动检测机制组成。这种机制是通过对适当的抽象模型进行直接或间接的状态枚举技术来实现的，从而证明模型中存在或者不存在所谓的“瑕疵”状态。定理证明则是运用数学推理和逻辑推论来证明系统的正确性。本文所讨论的就是模型检测方法中的限界模型检测方法及其相关的改进和应用。近些年来，基于可满足性求解（SAT）的限界模型检测方法作为基于BDD的模型检测方法的一种有效的补充，已经有了一定的发展。A. Biere等人最先提出了对于线性时序逻辑公式（LTL）的限界模型检测方法，进而，W.Penczek又提出了对于全局计算树逻辑（ACTL）的限界模型检测方法。由于模型检测方法具有很高的复杂性，因此，其效率问题始终倍受关注。论文第一个方面的重要贡献就体现在提高限界模型检测效率方面的相关研究上。我们对Penczek提出的限界模型检测方法进行了两方面的改进，以提高其求解效率。第一方面的改进是通过改进所需路径条数计算函数，将时序操作符EX和其它时序操作符区分开来，以减少编码时所需的迁移关系和变量数目；第二方面的改进则是采用统一路径编码的方式来简化公式的编码。通过这两方面的改进，公式在最坏情况下的编码复杂度得到了有效的降低。同时，我们还在工具BMV中实现了改进后的方法。随着实时系统的应用日益广泛，在对全局计算树逻辑的限界模型检测方法做了改进，提高了其求解效率以后，我们又将目光转移到了对实时系统的限界模型检测上。如何将限界模型检测方法高效的运用到对实时系统的检测当中成为了本文第二个方面的重要贡献。基于SAT的限界模型检测方法在对实时系统的模型和描述性质的公式进行编码时，需要对时间变量和时钟约束进行布尔编码，由于时间的连续性和不确定性，使得在对它进行布尔编码时，往往会相当的复杂，不仅耗费大量的时间，而且还不利于SAT的求解，即使是使用改进后的限界模型检测方法，整个验证过程的效率还是很低。所以，在对实时系统进行限界模型检测方面，我们转而考虑采用基于可满足性模块理论（SMT）的方法来对实时系统的模型和描述性质的公式进行编码。由于SMT可以直接处理基于整数或者实数的线性算术表达式，因此，我们可以直接用整型或者实型变量来表示时间变量，用线性算术表达式来表示时钟约束。与基于SAT的限界模型检测方法相比，基于SMT的限界模型检测方法在处理实时系统方面，不仅简化了编码过程，而且大大提高了求解效率。在此基础上，我们运用基于SAT的对全局计算树逻辑的限界模型检测方法中的改进思想，对基于SMT的实时系统的限界模型检测方法也做了相应的改进，使其求解效率较之改进前有了较大的提升。最后，我们就基于SAT的限界模型检测方法和基于SMT的限界模型检测方法以及它们的改进方法进行了一系列的实验对比。从实验结果可以看出，改进后的方法比改进前的方法在时间效率和空间效率上都有明显的提升，同时就实时系统来说，采用了SMT和限界模型检测相结合的方法以后，效率也比没有采用这两者的方法要高很多。

基于Yices对时间自动机的有界模型检测

随着工业化程度的提高，对模型的检测方法受到越来越大的重视。通常的检测方法有推理验证和模型检测。而相对于推理验证，模型检测由于其高度自动化的检测过程，在工业界有着更广泛的应用。 模型检测自从概念雏形开始之时，就受到状态爆炸问题的困扰。为了解决这个问题，不同的技术被提了出来。McMillan提出利用OBDD的符号模型检测方法在一定程度上解决了这个问题。另外，本文所主要讲述的有界模型检测，经大量的实践证明，对符号模型检测也是一个很好的补充。 由于问题的特殊性，科学家提出来不同的模型来描述不同情况的系统。由于时间自动机能够很好地描述异步系统，而且这种系统广泛地存在于现实生活中，对时间自动机这种特殊模型的验证方法的研究变得很有必要。另外，由于时间自动机带有实数域的时钟变量，这导致了时间自动机有一个无限域的状态迁移图。为了利用模型检测的方法对其进行验证，需要对时间变量进行预处理。一般的方法是把时钟所对应的时钟区或时钟域根据等价性，化为有限的域，相应地，把时间自动机转化为有限的状态迁移图。 为了避免在对时间自动机有界模型检测过程中对变量进行布尔编码以及对时间自动机模型中的时钟进行预处理，本文给出一个利用SMT工具进行的对时间自动机进行有界模型检测的方法。该方法的主要优点是无需将时间自动机中的时钟进行预处理，也不需要将模型中的变量进行布尔编码，只需将时间自动机转变为SMT工具可解的逻辑公式，利用SMT的高效求解来进行模型检测。实验结果表明，对于某些可达性性质的验证，这种方法的效率有一定的优势。

基于一阶迁移系统的限界模型检测工具实现

基于布尔可满足性(SAT)的限界模型检测是一种高效的模型检测方法，它具有快速查错，反例最小化等特点，已经成为学术界和工业界关注的热点。近些年出现了很多集成限界模型检测算法的验证工具，如ITC-IRST、卡内基梅隆大学(CMU)等多家科研机构联合开发的NuSMV工具；加利福尼亚大学伯克莱分校(UC Berkeley)、科罗拉多大学博尔德分校(CU Boulder)联合开发的VIS工具等。因此目前对于限界模型检测方法的研究和相关工具的设计与开发具有重要而广泛的意义。在进行限界模型检测的建模过程中，不同的工具采用了自定义的建模语言。如经典工具SPIN采用的建模语言是Promela语言，NuSMV采用的是自定义的NuSMV语言。随着系统验证规模的不断增大，建模语言的特点将会直接影响到建模的效率。例如采用NuSMV语言去建立一个网络通信协议模型会显得比较复杂和耗时，应用NuSMV语言去描述一个简单的数据链路层网络协议ABP协议(Alternating Bit Protocol)就不如采用Promela语言去描述显得直观和自然。 为了简化在限界模型检测过程中模型的建立过程，本文给出了一种采用基于一阶迁移系统语言描述的模型建立方法，并在一阶迁移系统语言中实现了通道的功能，从而增强了描述能力。在此基础上完成了一个以基于插值和k步归纳限界验证算法为核心的模型检测工具(BMCF)。最后利用该工具对常见的互斥协议，简单数据传输协议的性质进行了分析与验证。结果表明，利用该工具对系统进行建模具有方便直观的特点，并借助实现的验证算法能高效的检验安全性质的正确性，如果性质不成立工具会给出反例提示。