Time-delayed feedback control optimization for quasi linear systems under random excitations

A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to derive the stationary response of the system. Secondly, the control law is assumed to be velocity feedback control with time delay and the unknown control gains are determined by the performance indices. The response of the controlled system is predicted through solving the Fokker-Plank-Kolmogorov equation associated with the averaged Ito equation. Finally, numerical examples are used to illustrate the proposed control method, and the numerical results are confirmed by Monte Carlo simulation .

Simulation of Quasi-Linear Mesoscale Convective Systems in Northern China：Lightning Activities and Storm Structure

Two intense quasi-linear mesoscale convective systems（QLMCSs） in northern China were simulated using the WRF（Weather Research and Forecasting） model and the 3D-Var（three-dimensional variational） analysis system of the ARPS（Advanced Regional Prediction System） model.A new method in which the lightning density is calculated using both the precipitation and non-precipitation ice mass was developed to reveal the relationship between the lightning activities and QLMCS structures.Results indicate that,compared with calculating the results using two previous methods,the lightning density calculated using the new method presented in this study is in better accordance with observations.Based on the calculated lightning densities using the new method,it was found that most lightning activity was initiated on the right side and at the front of the QLMCSs,where the surface wind field converged intensely.The CAPE was much stronger ahead of the southeastward progressing QLMCS than to the back it,and their lightning events mainly occurred in regions with a large gradient of CAPE.Comparisons between lightning and non-lightning regions indicated that lightning regions featured more intense ascending motion than non-lightning regions;the vertical ranges of maximum reflectivity between lightning and non-lightning regions were very different;and the ice mixing ratio featured no significant differences between the lightning and non-lightning regions.

Transition From Hyper－Chaotic State to Quasi－Steady State in a Spailally Distributed Nonlinear System

The dynamic characteristic in a spatially distributed nonlinear system, a subset of lasers in an array of coupled lasers, has been studied and analysed numerically. The evolution, with the increasing coupling strength,from stable quiescent state to chaotic state, to hyper-chaotic state and, back to quasi-steady state has been observed in this system.

THE ESTIMATION OF SOLUTION OF THE BOUNDARY VALUE PROBLEM OF THE SYSTEMS FOR QUASI-LINEAR ORDINARY DIFFERENTIAL EQUATIONS

This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder.

Uniqueness of solution of a quasi-linear Reaction-diffusion system

In this paper,we consider nonnegative classical solutions of a Quasi-linear reaction-diffusion system with nonlinear boundary conditions.We prove the uniqueness of a nonnegative classical solution to this problem.

Establishment of infinite dimensional Hamiltonian system of multilayer quasi-geostrophic flow & study on its linear stability

A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms.

A Class of Quasi-Linear Riemann-Hilbert Problems for General Holomorphic Functions in the Unit Disk

In this paper, a class of quasi linear Riemann Hilbert problems for general holomorphic functions in the unit disk was studied. Under suitable hypotheses, the existence of solutions of the Hardy class H 2 to this problem was proved by means of Tikhonov's fixed point theorem and corresponding theories for general holomorphic functions.

THE INITIAL BOUNDARY VALUE PROBLEM FOR QUASI-LINEAR SCHRODINGER-POISSON EQUATIONS

In this article, the author studies the iuitial （Dirichlet.） boundary problem for a high field version of the Schroedinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schroedinger equations on the unit cube. h global existence and uniqueness is established for a solution to this problem.

A QMR-Type Algorithm for Drazin-Inverse Solution of Singular Nonsymmetric Linear Systems

In this paper, we propose DQMR algorithm for the Drazin-inverse solution of consistent or inconsistent linear systems of the form Ax=b where is a singular and in general non-hermitian matrix that has an arbitrary index. DQMR algorithm for singular systems is analogous to QMR algorithm for non-singular systems. We compare this algorithm with DGMRES by numerical experiments.

Decoupling Analysis for a Powertrain Mounting System with a Combination of Hydraulic Mounts

The existing torque roll axis(TRA) decoupling theories for a powertrain mounting system assume that the stiffness and viscous damping properties are constant. However, real-life mounts exhibit considerable spectrally varying stiffness and damping characteristics, and the influence of the spectrally-varying properties of the hydraulic mounts on the powertrain system cannot be ignored. To overcome the deficiency, an analytical quasi-linear model of the hydraulic mount and the coupled properties of the powertrain and hydraulic mounts system are formulated. The influence of the hydraulic mounts on the TRA decoupling of a powertrain system is analytically examined in terms of eigensolutions, frequency, and impulse responses, and then a new analytical axiom is proposed based on the TRA decoupling indices. With the experimental setup of a fixed decoupler hydraulic mount in the context of non-resonant dynamic stiffness testing procedure, the quasi-linear model of the hydraulic mount is verified by comparing the predictions with the measurement. And the quasi-linear formulation of the coupled system is also verified by comparing the frequency responses with the numerical results obtained by the direct inversion method. Finally, the mounting system with a combination of hydraulic mounts is redesigned in terms of the stiffness, damping and mount locations by satisfying the new axiom. The frequency and time domain results of the redesigned system demonstrate that the torque roll axis of the redesigned powertrain mounting system is indeed decoupled in the presence of hydraulic mounts (given oscillating torque or impulsive torque excitation). The proposed research provides an important basis and method for the research on a powertrain system with spectrally-varying mount properties, especially for the TRA decoupling.

BLOW-UP ESTIMATES FOR A NON-NEWTONIAN FILTRATION SYSTEM

The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blowup estimates for a class quasi-linear reaction-diffusion systems ( non-Newtonian filtration systems) are established, which extends the result of semi-linear reaction diffusion( Fujita type) systems.

Parallel difference schemes with interface extrapolation terms for quasi-linear parabolic systems

In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed. Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism.

Difference schemes with intrinsic parallelism for quasi-linear parabolic systems

The boundary value problem for quasi-linear parabolic system is solved by the finite difference method with intrinsic parallelism The existence and uniqueness and convergence theorems of the discrete vector solu tions of the nonlinear difference system with intrinsic parallelism are proved The limiting vector function is just the unique generalized solution of the original problem for the parabolic system

Global Existence of Small Solutions for Cubic Quasi-linear Klein-Gordon Systems in One Space Dimension

In this paper, we consider a system of two cubic quasi-linear Klein-Gordon equations with different masses for small, smooth, compactly supported Cauchy data in one space dimension. We show that such a system has global existence when the nonlinearities satisfy a convenient null condition. Our results extend the global existence proved by Sunagawa recently under the non-resonance assumption to that under the resonance assumption.

M-D Riemann problem for a class of quasilinear hyperbolic system and its perturbation

In this note the Cauchy problem of quasilinear hyperbolic system will be discussed U_t+F(U)_x+G(U)_y=0, (1)where U=~t(u, v), F=~t(u^2, uv), G=~t(uv, v^2). The system is nonstrictly hyperbolic andpossibly arises in some physical problems such as oil recovery and elastic theory. The initialdata of our porblem are given

The Holderian solution and its singularity propagation for a class of system of quasi-linear partial differential equations

where U and F are the vector-valued functions which are defined on R+×RN and R+×RN×RN,respectively, U=（u1,…,uN）, F=（f1,…,fN）, =（x1,……,x）N. Moreover, F is smooth enough, andits derivatives of all orders are boundary on R×K. K is any compact set in R2N.Obviously,

华北两类产生极端强天气的线状对流系统分布特征与环境条件

华北线状对流系统精细气候分布及其所产生的极端天气特征尚不清楚,本研究利用雷达拼图资料和客观识别方法普查2013—2018年华北171例线状对流系统的时、空分布特征,根据其所致强对流天气的统计结果,发现华北地区至少有2类线状对流系统,分别产生极端强雷暴大风和极端强降水。分析了这2类线状对流系统的环流形势、环境条件、地形作用和关键中尺度系统地面冷池等的特征。主要结论如下:华北线状对流系统的空间分布尤其是初始形成位置与大地形关系密切,京津冀的太行山和燕山山脚区域为其中的一个高发区;2类线状对流系统发生月份、空间尺度、移动速度、形成时刻和维持时间等都具有显著差异;2类线状对流系统的环流背景、环境条件和冷池也差别明显。强雷暴大风型线状对流系统的环境大气斜压性强,中层干和大的垂直减温率造成的最优对流有效位能、下沉对流有效位能大值区是产生极端大风的重要环境条件,地面强冷池以及0—3 km风垂直切变对前向传播起到了重要作用。强降水型线状对流系统产生的降水极端性较前一类型更为凸出,天气尺度强迫相对较弱,水汽条件极其充沛,地面弱冷池或地形与低层南风气流相互作用维持的后向传播是其发展和缓慢移动的主要机制,也是产生极端强降水的直接原因。

反应烧结碳化硅过程的数学模型

考虑不同因素的影响 ,建立了反应烧结碳化硅反应烧结过程的一组数学模型 。

飞行器控制的伪线性系统方法——第一部分:综述与问题

首先将非线性控制方法归纳成三类:基于李雅普诺夫泛函的设计方法、基于最优控制思想的设计方法和以线性为主导的设计方法,并对此三类方法进行了简略的综述。然后进一步在此类划分的框架下概述了飞行器控制的非线性方法,并引入了伪线性系统的概念。最后介绍了卫星姿态与轨道控制、飞行器制导与控制中的六类典型飞行器控制问题的二阶伪线性系统描述。