李亚普诺夫方法的发展与历史性成就——纪念李亚普诺夫的博士论文“运动稳定性的一般问题”发表一百周年

本文论述了李亚普诺夫方法的发展,全文共分七部分:1 李亚普诺夫方法产生的历史背景;2 在李亚普诺夫原数学模式中的发展;3 在反馈系统中的发展与应用;4 李亚普诺夫方法与时变、不确定系统;5 在理论上的进一步发展;6 比较原理与李亚普诺夫方法;7 结束语。     

含二维临界部分系统的李亚普诺夫函数构造

含二维临界部分系统的李亚普诺夫函数构造苗原（清华大学计算机系北京１０００８４）李春文（清华大学自动化系北京１０００８４）关键词中心流形,稳定性,非线性系统,李亚普诺夫函数．收稿日期１９９５－１０－０６１引言李亚普诺夫函数不仅是重要的判稳工具,还与使系...     

基于条件李亚普诺夫指数的混沌系统的脉冲同步研究

基于条件李亚普诺夫指数,对混沌系统的脉冲同步形式和同步范围进行了研究,突破了传统的基本假设．计算机仿真证明了该方法的有效性和正确性．此外,作为该方法的重要基础,本文给出脉冲同步系统的条件李亚普诺夫指数计算方法．     

基于最大李亚普诺夫指数的改进混沌时间序列预测

分析了基于最大李亚普诺夫指数的混沌时间序列预测方法,提出了一种选取重构相空间中的多个邻近参考向量来提高预测精度的改进方法．对洛伦兹混沌系统产生的时间序列进行了预测,结果表明改进方法比原方法的预测精度要高．讨论了噪声和参考邻近点数对预测结果的影响．应用改进方法预测实际的交通流量时间序列的平均相对误差在8%以下,说明了改进方法的有效性．     

基于李亚普诺夫法控制的PWM整流器仿真研究

讨论了基于李亚普诺夫稳定定理的PWM整流器控制方法,并以此控制方法进行整流器仿真,给出了仿真结果。结果表明:它不仅性能优良,而且使系统具有绝对稳定性。     

非线性定常系统及其定常Lyapunov函数的多项式等价类

非线性定常系统及其定常Ｌｙａｐｕｎｏｖ函数的多项式等价类苗原李春文杜继宏（清华大学自动化系北京１０００８４）关键词稳定性,非线性多项式系统,李亚普诺夫函数．收稿日期１９９５－０５－１６１引言李亚普诺夫第二方法作为处理系统稳定性问题的最主要的方法之一已...     

Chen混沌系统的一种自适应同步方法

混沌系统的研究在国内外正在广泛的开展,如何使得对混沌系统的控制达到良好的控制效果构成了问题的关键.由于Chen混沌系统具有的参数不确定性,以至于常规的控制方法很难实现对Chen混沌系统的控制,讨论了一种参数可调节的自适应同步设计方法.设计出了可以使两个同结构的Chen系统状态渐近同步的自适应控制器,其参数调节律由Lyapunov稳定性理论来确定.最后进行数字仿真,仿真结果表明了这种方法的有效性和实用性.     

Riccati代数方程中矩阵P与R,Q关系的研究

本文对Riccati代数方程中矩阵P与R,Q的关系进行了研究.给出了矩阵R、Q变化时方程解P的变化范围.这对最优控制、鲁棒控制、容错控制及H∞控制等有着重要的意义.     

基本积分型李亚普诺夫函数的直接自适应神经网络控制

针对一类具有下三角形函数控制增益矩阵的非线性系统,基于滑模控制原理,并利用多层神经网络的逼近能力,提出了一种直接自适应神经网络控制器设计的新方案.通过引入积分型李亚普诺夫函数及残差与逼近误差和的上界函数的自适应补偿项,证明了闭环系统是全局稳定的,跟踪误差收敛到零.     

基于增益协调方法的非线性控制器设计

为了寻求结构简单、易于进行稳定性分析的非线性控制器的设计方法,提出一种基于增益协调的非线性控制器设计方法理论。该控制器可以逼近很多复杂的非线性控制器,并具有相同的控制效果。该方法与模糊控制器的控制效果进行比较,说明了基于增益协调的非线性控制器简单、易于实现,同时更具便于调节的优点。同时基于李亚普诺夫稳定性理论,对例题中设计出的增益协调控制器的稳定性给予证明。结合桌飞控系统舵机控制实例,说明了该方法的实用性。     

Boundary control with integral action for hyperbolic systems of conservation laws: Stability and experiments

A strict Lyapunov function for boundary control with integral actions of hyperbolic systems of conservation laws that can be diagonalised with Riemann invariants, is presented. The time derivative of this Lyapunov function can be made strictly negative definite by an appropriate choice of the boundary conditions and the integral control gains. Previous stability results are extended to guarantee the local convergence of the state towards a desired set point. Furthermore, the control can be implemented as a feedback of the state measured only at the boundaries. The control design method is illustrated with a hydraulic application, namely the level and flow regulation in a reach of the Sambre river and in the micro-channel of Valence, respectively through simulations and experimentations.     

Analysis and control of the jump modes behavior of 2-D singular systems—Part I: Structural stability

This paper considers the problem of structural stability of 2-D singular systems. Firstly, some properties of structural stability of 2-D general singular systems are presented. Sufficient and necessary conditions for the structural stability of the 2-D singular systems are given. Then, by extending the Lyapunov approach for the structural stability of 1-D continuous singular systems to the discrete case, a generalized Lyapunov equation approach to the analysis of the structural stability of 2-D singular Roesser models (2-D SRM) is proposed. The existence of a solution to the generalized Lyapunov equation gives a sufficient condition for the structural stability of the 2-D SRM.     

On Stability of Immune Protection Model with Regard for Damage of Target Organ: The Degenerate Liapunov Functionals Method

Stability problem for G. I. Marchuk immune protection system is considered. The degenerate Lyapunov functional method is used. Sufficient stability conditions are obtained for the system taking into account influence of a damaged organ on the immune response.     

Stability of discrete-time systems joined with a saturation operator on the state–space: Generalized form of Liu-Michel’s criterion

A novel criterion for the global asymptotic stability of discrete-time systems in a state–space realization using saturation arithmetic was previously given by Liu and Michel. In their approach, as in most (or probably all) existing approaches, the matrix is assumed to be symmetric. In this communique, it is shown that their approach is such as to be extended to allow the use of an unsymmetric matrix . Taking note of this, a more general form of their criterion is presented. A modified form of the criterion is also presented. Examples show the effectiveness of the generalized approach. To the best of author’s knowledge, this communique is the first report of exploiting an unsymmetric to obtain a stability condition with reduced conservatism.     

一个新混沌系统的自适应模糊同步

本文基于Takagi-Sugeno(T-S)模糊模型,研究了混沌系统的自适应同步。基于T-S模糊模型重构了混沌系统,推导了在衰减率α下,自适应同步全局渐近稳定的充分条件;同时,在驱动系统参数未知的情况下,使用自适应参数调节律,得到响应系统参数的估计值。设计的模糊控制器均由线性函数构成,结构简单,规则少,有利于实际应用中构造控制器。数值仿真结果验证了方法的有效性。     

图形检索系统的设计与实现

随着信息技术和计算机的普及,如何更有效的利用这些技术来推动教育的发展引起了人们的普遍关注。本文以中学数学教育为切入点,设计并实现了一种图形检索系统,模拟计算机自动推理的方式智能化解题系统,并探讨了系统实现过程中的数据存储、动态作图、数据检索等关键技术。     

嵌入式系统的发展趋势

本文描述了嵌入式系统的特点、发展现状及发展趋势。     

Validating Real-Time Constraints in Heterogeneous Multiprocessor and Distributed Systems

A heterogeneous system or distributed system typically contains different types of processors. Some jobs can execute on certain types of processors but not other types. Processors of different types may have different speeds. We present several worst-case upper bounds and efficient algorithms for determining the completion times of independent jobs that have arbitrary timing constraints and variable execution times and are scheduled on available processors dynamically in a priority-driven manner. Bounds and algorithms take into account the effects of nonmigratability, nonpreemptability and different levels of migratability.