一阶拟线性双曲型方程组慢时间尺度下的零松弛极限

本文考虑慢时间尺度下带松弛时间源项的高维一阶拟线性双曲型方程组Cauchy问题的光滑解,这个方程组具有非守恒的形式;假设它是部分耗散的对称双曲组,当松弛时间趋于零时,它在形式上趋于一个两阶非线性抛物型方程组.在双曲型方程组满足一些结构性的假设下,本文得到了两个收敛性的结果.对于大初值,本文证明了双曲型方程组在一个对松弛时间一致的时间区间上的收敛性,当初值在常数平衡态附近变化时,证明了光滑解关于时间的一致整体存在性和双曲型方程组的整体收敛性.本文也给出一些有物理背景的例子来作为这些结果的应用.     

变阶可解族的带权逼近与插值逼近

本文讨论了变阶可解逼近族的插值逼近和带权逼近(权在插值点集Z上趋于无穷而在Z外为1)的关系.指出对变阶可解族而言,当逼近解为非亏损时,稠密性假设是自然满足的,且此时的最佳插值逼近等于该带权最佳逼近的极限.     

一类平均场随机微分方程的遍历性（英文）

本文研究了一类一维带平均场的非时齐随机微分方程.在一定条件下,我们证明了方程唯一解的遍历性.进一步地,当平均场强度趋于0时,我们还证明了方程的解和平稳分布分别几乎一致、依Wasserstein距离收敛于相应无平均场方程的解和平稳分布.     

非最小相位高超声速飞行器自适应动态面控制

研究存在参数不确定和非最小相位特性的吸气式高超声速飞行器的控制律设计问题.通过深入分析被控对象的动力学特点,提出了一种新型设计思想.将系统分为速度子系统和俯仰动力学子系统分别进行设计.针对速度子系统,设计自适应动态逆控制;针对非最小相位俯仰动力学子系统,设计高增益自适应动态面控制.稳定性分析表明,系统的跟踪误差是一致最终有界的,其它状态是有界的.最后的数值仿真验证了该方法的有效性.     

带线性记忆和结构阻尼的非自治Kirchhoff型板方程的一致吸引子

本文试图研究带线性记忆和结构阻尼的非自治Kirchhoff型板方程的一致吸引子的存在性.为此,引入一个新的变量η,将先验估计与收缩函数的方法相结合,证明一致有界吸收集和一致渐近紧性,最终得到一致吸引子的存在性.     

常系数非齐次线性微分方程组的初等解法

利用初等变换将常系数非齐次线性微分方程组化为由若干个相互独立的高阶常系数非齐次线性微分方程组成的方程组,再利用高阶常系数齐次线性微分方程的特征根法和非齐次方程的待定系数法求该方程组的基本解组及特解,最后通过初等变换求原方程组的基本解组及特解,从而可求出其通解.     

各向异性的群集行为分析

探究欧氏空间中一类具有吸引/排斥函数的各向异性群集系统的集结属性,将个体间的耦合矩阵进行了一定的推广.该模型的耦合矩阵更具普遍意义.结果表明:在耦合权值满足一定平衡条件的情况下,群集成员将在有限时间内聚集并形成一个以群集的加权中心为球心的紧凑的有界群体.仿真实例进一步表明了群集个体最终进入并驻留在群集加权中心的有界区域内.     

基于数据包络分析的并行生产系统效率评价方法

数据包络分析(DEA)是一种评价具有多投入、多产出决策单元的相对效率的线性规划方法.在现实世界中,决策单元有时呈现出由多个独立子系统构成的复杂并联网络系统,各子系统的投入/产出之和构成了系统的总投入/产出.目前,用于评价这种具有并联网络生产系统相对效率的模型主要有三种:网络DEA模型、多部门DEA模型和关联DEA模型.现有这些模型的基本特性和相互关系存在着不足,即子系统的效率分解和优化指数不唯一.为解决这一问题,提出了改进的并联DEA模型,并采用加拿大银行系统实例来说明所提出模型的合理性和有效性.     

一类非线性等级结构种群控制模型解的适定性

分析一类具有个体年龄等级差异的非线性种群系统模型解的适定性问题.运用特征线法、积分不等式和不动点原理证明了系统非负解的存在唯一性和有界性,以及解对控制变量的一致连续性.拓展了常见的年龄结构系统基本理论.为研究种群的长期演化和调控问题奠定基础.     

含有未知输人及非强可检测子系统的线性切换系统的观测器设计

主要研究含有未知输入的线性切换系统的观测器设计问题.系统中包含有强可检测和非强可检测的子系统.首先,给出了状态及输出的坐标变换,通过坐标变换,系统的一部分子系统将不受未知输入的影响.其次,当未知输入的扰动矩阵线性相关,可以设计出不含状态跳跃的观测器.更一般的,如果扰动矩阵线性无关,可以设计含有状态跳跃的观测器.基于平均驻留时间的假定,可以得到重构状态的误差指数收敛于0.最后给出数值仿真验证理论结果.     

错误系统结构的分解变换研究

对于错误系统的结构分解,需要先弄清楚错误系统的结构,再把该错误系统以某种基本结构分解成若干子系统,然后对子系统又以某种基本结构分解成下一层次的若干子系统,如此下去,直到所有子系统都为基本结构子系统为止.在此基础上,研究以串联、并联、扩缩、蕴含、反馈和其它型等六种基本型为基础的分解变换的分解方式,分解类型.同时采用图说明相应变换,采用系统结构与错误函数定量描述变换的逻辑规律,利用结构与功能的关系定量描述系统结构与错误的关系,最后给出了变换体系.     

Two Methods of Simulator Coupling

Modelling and simulation of complex engineering systems are often relieved by a modular approach in which the global system is decomposed into subsystems. Advantages arise from independent and parallel modelling of subsystems over easy exchange of the resulting modules to the use of different software for each module. However, the modular simulation of the global system by coupling of simulators may result in an unstable integration, if an algebraic loop exists between the subsystems. This numerical phenomenon is analyzed and two methods of simulator coupling which guarantee stability for general systems including algebraic loops are introduced. Numerical results of the modular simulation of a multibody system are presented.     

Estimates of reachable sets of multidimensional control systems with nonlinear interconnections

The paper is devoted to the problem of constructing external estimates for the reachable set of a multidimensional control system by means of vector estimators. A system is considered that permits a decomposition into several independent subsystems with simple structure (for example, linear subsystems), which are connected to each other by means of nonlinear interconnections. For each of the subsystems, an external estimate of the reachable set is assumed to be known; this estimate is representable in the form of a level set of some function satisfying a differential inequality. An estimate for the reachable set of the combined system is constructed with the use of estimates for subsystems. The method of deriving the estimates is based on constructing comparison systems for analogs of vector Lyapunov functions (value functions).     

DTZ model with independent subsystems

Data envelopment analysis (DEA) is a mathematical programming approach to assess relative efficiency of a group of decision-making units. In view of the defects of existing models in evaluating efficiency of the system with P independent subsystems, Yang et al. [10] introduced YMK model with the assumption that decision-making unit (DMU) is independent of each other. But in some production systems, decision-making units usually have some relationships in this way or that. In this paper, DEA model is given by assuming that DMUs can cooperate with others in its subgroups. Some property and the efficiency relationship of the whole system and its subsystems are given.     

Synthesis of a control in a non-linear dynamical system based on decomposition

A non-linear controllable dynamical system with many degrees of freedom, described by Lagrange equations of the second kind, is considered. Geometric constraints are imposed on the magnitudes of the controls. It is assumed that, in the equations of motion, the kinetic energy matrix is close to a certain constant diagonal matrix. It is possible, for example, to reduce the equations of motion of robots, the drives of which have large gear ratios, to a system of this kind. A problem is formulated on the transfer of a system in a finite time from a specified initial state to a final state with zero velocities. The method of decomposition [1] is used to construct the equations. Sufficient conditions are found subject to which the maximum values of the non-linear terms in the equations of motion do not exceed the permissible magnitudes of the controls. In this case, non-linearities are treated as limited perturbations and the system is decomposed into independent, linear, second-order subsystems. A feedback control is specified for these subsystems which guarantees that each of them is brought into the final state for any permissible perturbations. The control has a simple structure. Applications of the proposed approach to problems in the control of manipulating robots are considered.     

On minimal decomposition of p-adic polynomial dynamical systems

A polynomial of degree ?2 with coefficients in the ring of p-adic numbers Zp is studied as a dynamical system on Zp. It is proved that the dynamical behavior of such a system is totally described by its minimal subsystems. For an arbitrary quadratic polynomial on Z₂, we exhibit all its minimal subsystems.     

Hybrid decentralized maximum entropy control for large-scale dynamical systems

In the analysis of complex, large-scale dynamical systems it is often essential to decompose the overall dynamical system into a collection of interacting subsystems. Because of implementation constraints, cost, and reliability considerations, a decentralized controller architecture is often required for controlling large-scale interconnected dynamical systems. In this paper, a novel class of fixed-order, energy-based hybrid decentralized controllers is proposed as a means for achieving enhanced energy dissipation in large-scale lossless and dissipative dynamical systems. These dynamic decentralized controllers combine a logical switching architecture with continuous dynamics to guarantee that the system plant energy is strictly decreasing across switchings. The general framework leads to hybrid closed-loop systems described by impulsive differential equations. In addition, we construct hybrid dynamic controllers that guarantee that each subsystem–subcontroller pair of the hybrid closed-loop system is consistent with basic thermodynamic principles. Special cases of energy-based hybrid controllers involving state-dependent switching are described, and an illustrative combustion control example is given to demonstrate the efficacy of the proposed approach.     

Modelling and analysis of thermal networks through subnetworks for multizone passive solar buildings

An efficient method is presented for the computer analysis in the frequency domain of multizone passive solar buildings. This method models heat conduction and convection between rooms, heat flows which are often not accounted for in order to reduce computation time. Heat transfer through a building is modelled by a thermal network. Massive walls are represented as two-port elements, analogous to non-inductive electrical transmission lines. Nodes representing exterior surfaces, whose temperatures do not have to be explicitly determined, are eliminated by the Norton theorem. The resulting simplified, but still complex networks, are split into subnetworks corresponding to rooms by removing a few simple components; the solutions for the subnetworks are found by means of the nodal formulation and are then coupled to give the system solution, without ever having to solve directly the initial complex network. There are no errors introduced by this decomposition process. This significantly simplifies the analysis of the building network and provides physical insight into the modelling and coupling of its subsystems.     

On Decomposition of Algebraic PDE Systems into Simple Subsystems

In this paper we present an algorithmization of the Thomas method for splitting a system of partial differential equations and (possibly) inequalities into triangular subsystems whose Thomas called simple. The splitting algorithm is applicable to systems whose elements are differential polynomials in unknown functions and polynomials in independent variables. Simplicity properties of the subsystems make easier their completion to involution. Our algorithmization uses algebraic Gröbner bases to avoid some unnecessary splittings.