一类混杂系统的混杂时态Petri网模型

本语文为一类混杂系统的建模提出了混杂时态Ｐｅｔｒｉ网（ＨＴＰＮ）模型,在该模型下,系统的微观连续行为由混杂时态Ｐｅｔｉ网变迁对应的微分方程描述,宏观行为由变迁对应的离散事件描述,同时在该模型的基础上,讨论了混杂系统的宏观及微观运行问题,并提出了佥状态轨迹的概念来描述系统的动态行为。最后给出一实例来说明模型的合理性和应用。     

一类多变量非线性动态系统的模糊自适应控制

对一类非线性多变量未知动态系统，提出了一种模糊处在适应控制策略。证明了该控制算法能保证闭环系统稳定，跟踪误差收敛。     

一类非线性系统的模糊变结构控制

研究了一类非线性系统的模糊变结构控制问题，并给出了稳定性证明。通过将非线性系统化为多个精确T—S模型来建立非线性系统精确的T—S模糊模型，将模糊理论与成熟的线性变结构控制理论相结合设计一种模糊变结构控制器，用Lyapunov稳定性理论证明该控制器能确保模糊动态模型全局渐近稳定，从而使非线性系统稳定。仿真结果表明了该设计方法的有效性。     

一类线性不可观非线性系统的动态输出反馈镇定

本文研究一类不可观非线性系统的动态输出反馈镇定,基于逼近渐近稳定性的概念,给出了动态输出反馈可镇定的充分条件,本文主要结果的直接推论是零动太逼近渐近稳定的最小相位系统能用动态输出反馈镇定,本文的方法也能处理非最小相位系统。     

一种新型时滞系统鲁棒控制器设计方法

针对一类用模糊动态模型描述的非线性时滞系统，提出一种基于模糊性能评估器的新型鲁棒控制方案，模糊性能评估器用于检验模糊模型及其控制率的有效性，以线性矩阵不等式的形式，给出了模糊性能评估器和模糊控制器存在的充分条件；分析了闭环控制效果与模糊性能评估器性能之问的关系，从而说明该方法为模糊控制系统提供了一种无损调试方法，最后以CSTR系统为例，通过仿真验证了该方法的有效性。     

一类仿射非线性网络控制系统的稳定性分析

利用采样数字控制系统的方法分析了一类混杂动态系统模型描述的仿射非线性网络控制系统的稳定性问题.针对一类仿射非线性对象和线性数字控制器组成的网络控制系统，考虑了网络诱导延时对系统稳定性的影响，得到了仿射非线性网络控制系统一致渐近稳定的条件．仿真实例验证了理论分析的正确性．     

一种在线建模方法的研究

针对一类系统提出了一种通用性较强的建模与决策方法以及在线生成系统模型的 途径.该法可广泛用于静态、动态、线性与非线性系统的建模与决策.     

一类相似组合时变非线性系统的全息稳定化

研究一类相似组合时变非线性系统。对由单输入子系统互联而得的相似组合时变非线性系统，采用增加辅助控制器的方法给出了用非光滑控制进行全息稳定化的条件，结果表明相似结构简化组合系统的分析设计，全息控制能简化控制器的工程设计。最后通过一个数值例子予以说明。     

一种基于神经网络在线逼近器的非线性鲁棒故障诊断方法

针对一类不确定非线性动态系统，提出了一种基于神经网络在线逼近结构的鲁棒故障 检测方法．该方法通过构造神经网络通过在线逼近结构学习非线性故障特性来监测动态系统 的反常行为,当故障发生时，在线估计器可逼近各种可能的未知故障，然后对其进行诊断和 适应．神经网络权重的在线学习律没有持续激励的要求，并采用Lyapunov稳定性理论保证了 闭环误差系统一致最终有界稳定．     

一类不可逆系统的非线性控制及预期动力学方程的选取

改进了非线性控制的逆系统方法，使之适用于一类典型的不可逆系统的控制器设计；提出了一族预期动力学方程及其参数的选取规则，简化了非线性控制系统的设计，使之满足稳定性，动态性能，静态性能和鲁棒性等方面的要求。仿真结果证实了本文结论的正确性。     

A fully deterministic micro–macro simulation of complex flows involving reversible network fluid models

Micro–macro models associate the coarse-grained molecular scale of the kinetic theory to the macroscopic scale of continuum mechanics. The conservation equations are solved along with the microscopic equation or the so-called Fokker–Planck equation. In this paper, a micro–macro approach based on the separated representation introduced in 2 and 3 with the Stream-Tube method 10, 11, 12, 21 and 22 is implemented to study the main features of fiber and polymer networks solutions in complex flows. The Fokker–Planck equation, that defines the fluid microstructure, is solved using a separated representation strategy and is coupled to the macroscopic equations through the macroscopic extra-stress tensor evaluated at the microscopic level. Then, the flow kinematics is solved by applying the Stream-Tube method.     

Perspectives on the design and control of multiscale systems

New applications in materials, medicine, and computers are being discovered where the control of events at the molecular and nanoscopic scales is critical to product quality, although the primary manipulation of these events during processing occurs at macroscopic length scales. This motivates the creation of tools for the design and control of multiscale systems that have length scales ranging from the atomistic to the macroscopic. This paper describes a systematic approach that consists of stochastic parameter sensitivity analysis, Bayesian parameter estimation applied to ab initio calculations and experimental data, model-based experimental design, hypothesis mechanism selection, and multistep optimization.     

Micro-macro Kolmogorov–Fokker–Planck models for a hard-sphere gas

Using a stochastic microscopic model of a rigid-sphere gas in a phase space, which is diffusive in the velocity space and valid at moderate Knudsen numbers, macroscopic equations of gas dynamics are derived, which are different from the system of Navier–Stokes equations or quasi-gasdynamic systems. The main pecularity of our derivation is more accurate velocity averaging due to the analytical solution of stochastic differential equations with respect to the Wiener measure, which describes our original meso model. The problem of a shock-wave front is used as an example showing that such an approach yields a greater and thus more realistic diffusion of the front than the one based on the Navier–Stokes equation. The numerical solution is based on a “discontinuous” particle method well suited for supercomputer applications.     

Modelling the plastic anisotropy of metals

Summary This work is an overview of available constitutive laws used in finite element codes to model elastoplastic metal anisotropy behaviour at a macroscopic level. It focuses on models with strong links with the phenomena occurring at microscopic level. Starting from macroscopic well-known models such as Hill or Barlat's laws, the limits of these macroscopic phenomenological yield loci are defined, which helps to understand the current trends to develop micro-macro laws. The characteristics of micro-macro laws, where physical behaviour at the level of grains and crystals are taken into account to provide an average macroscopic answer are described. Some basic knowledge about crystal plasticity models is given for non-specialists, so every one can understand the microscopic models used to reach macroscopic values. The assumptions defining the transition between the microscopic and macroscopic scales are summarized: full constraint or relaxed Taylor's model, self-consistent approach, homogenisation technique. Then, the two generic families of micromacro models are presented: macroscopic laws without yield locus where computations on discrete set of crystals provide the macroscopic material behaviour and macroscopic laws with macroscopic yield locus defined by microscopic computations. The models proposed by Anand, Dawson, Miehe, Geers, Kalidindi or Nakamachi belong to the first family when proposals by Montheillet, Lequeu, Darrieulat, Arminjon, Van Houtte, Habraken enter the second family. The characteristics of all these models are presented and commented. This paper enhances interests of each model and suggests possible future developments.     

基于序列分解的复杂系统的时序预测方法

现实中的时序数据，往往取自于复杂系统，表现出长记忆效应与短时不规则波动同时并存。传统的时序数据的分析和预测方法一般对不同层次的影响不加以区分，而是为其建立一个统一的模型，这使得在对复杂系统建模时需要用大量的参数予以表征，影响预测效率与精度。为此采用新的方法，将序列数据本身进行多平滑因子分解，对分解后的序列进行多尺度的采样并分别建模、预测，最后将结果整合。该方法应用于股票的实验表明，即使对起伏波动很大的时间序列，也能够得到较好的预测结果。     

Stable lattice Boltzmann schemes with a dual entropy approach for monodimensional nonlinear waves

We follow the mathematical framework proposed by Bouchut (2003) [22] and present in this contribution a dual entropy approach for determining equilibrium states of a lattice Boltzmann scheme. This method is expressed in terms of the dual of the mathematical entropy relative to the underlying conservation law. It appears as a good mathematical framework for establishing a “H-theorem” for the system of equations with discrete velocities. The dual entropy approach is used with D1Q3 lattice Boltzmann schemes for the Burgers equation. It conducts to the explicitation of three different equilibrium distributions of particles and induces naturally a nonlinear stability condition. Satisfactory numerical results for strong nonlinear shocks and rarefactions are presented. We prove also that the dual entropy approach can be applied with a D1Q3 lattice Boltzmann scheme for systems of linear and nonlinear acoustics and we present a numerical result with strong nonlinear waves for nonlinear acoustics. We establish also a negative result: with the present framework, the dual entropy approach cannot be used for the shallow water equations.     

Generalized Hamiltonian representation of thermo-mechanical systems based on an entropic formulation

In this work, we present an approach to construct generalized Hamiltonian representations for thermo-mechanical systems. Using entropic formulation of thermodynamic systems, the construction is applied to a class of thermo-mechanical systems. The proposed approach leads to an explicit expression of the dissipation along the trajectories of the dynamics. The considered thermo-mechanical systems are, in a thermodynamical sense, systems for which the dynamics of the extensive variables are functions of the intensive variables with respect to an entropic formulation. Using the entropy as the storage function, the dissipative structures of an analogue to a port-controlled Hamiltonian (PCH) representation are identified with irreversible phenomena, while the conservative structures are identified with reversible or isentropic phenomena. Examples are presented to illustrate the application of the proposed methodology, including a reacting system.     

A separation of scales homogenization analysis for the modelling of calcium leaching in concrete

Calcium leaching in concrete is highly influenced by the presence of aggregates. We present in this work a modelling framework of calcium leaching which accounts for this fact. Starting from the microscopic point of view, the method consists of the derivation of the macroscopic equation governing the average concentration field in the equivalent medium as well as the determination of the macroscopic transport parameters. In fact, the homogenization method used in this work is based on a separation of scales approach and allows to estimate the diffusion and the tortuosity tensors to be introduced in the macroscopic formulation of the mass conservation of calcium in the liquid phase. In this first attempt, we show that these estimates depend strongly on the morphological parameters of the microstructure which represent the geometry of the domain occupied by the phase in which the diffusion process takes place. The problem of numerically integrating the equations at hand is addressed within the context of the finite element method. Finally, numerical simulations are compared with our experimental results on cement paste, mortar and concrete.     

Computational networks and systems – homogenization of variational problems on micro-architectured networks and devices

Networked materials and micro-architectured systems gain increasingly importance in multi-scale physics and engineering sciences. Typically, computational intractable microscopic models have to be applied to capture the physical processes and numerous transmission conditions at singularities, interfaces and borders. The topology of the periodic microstructure governs the effective behaviour of such networked systems. A mathematical concept for the analysis of microscopic models on extremely large periodic networks is developed. We consider microscopic models for diffusion–advection–reaction systems in variational form on periodic manifolds. The global characteristics are identified by a homogenization approach for singularly perturbed networks with a periodic topology. We prove that the solutions of the variational models on varying networks converge to a two-scale limit function. In addition, the corresponding tangential gradients converge to a two-scale limit function for vanishing lengths of branches. We identify the variational homogenized model. Complex network models, previously considered as completely intractable, can now be solved by standard PDE-solvers in nearly no time. Furthermore, the homogenized coefficients provide an effective characterization of the global behaviour of the variational system.