控制非线性动力系统的混沌现象

控制混沌是一个新的概念。本文对混沌系统的控制，同步及反控制等问题给予综合介绍和评述，指出混沌控制这一新的令人鼓舞而且颇有起色的研制方向无论在理论还是在应用方面都具有十分诱人的前景。这一英新的科研和学术上的挑战正在向数学，物理，工程，以及多方面的交错学科中从事尖端研究的科学工作者们提出越来越多和越来越深刻物课题，因而特别应该引起非线性动力系统和工程控制论专家们足够的重视。     

一类混沌动态系统的图形演算

研究非线性混沌动态系统的图形自动演算问题。通过构建统一的自动演算环境，对Duffing方程从建模，实验到结果分析的全过程进行了图形演算。本强调数据的可视化处理，具有对复杂系统进行智能化多参数自动迭代运算的能力。     

基于线性搜索的混沌优化及其在非线性约束优化问题中的应用

提出基于线性搜索的混沌优化方法,利用混沌变量的特定内在随机性和遍历性来跳出局部最优点,而线性搜索可以提高局部空间的搜索速度和精度。结合精确不可微罚函数求解非线性约束优化问题。仿真结果表明,该算法简单易行,求解精度、收敛速度和可靠性较高,是解决优化问题一种有效方法。     

动态个体反恶化混沌粒子群优化算法

为防止粒子群优化算法陷入局部最优,引入个体反恶化和混沌机制,设计一种个体逐步反恶化的粒子群优化算法公式,提出动态个体反恶化混沌粒子群优化算法,使粒子摆脱局部最优,动态寻找全局最优值.采用多个著名标准测试函数进行实验,结果表明:本方法在不同情况下都超越其他著名粒子群优化改进算法.     

Two-Stage Algorithm for Estimation of Nonlinear Functions of State Vector in Linear Gaussian Continuous Dynamical Systems

Journal of Computer and Systems Sciences International - This paper focuses on the optimal minimum mean square error estimation of a nonlinear function of state (NFS) in linear Gaussian...     

Learning Linear and Nonlinear PCA with Linear Programming

An SVM-like framework provides a novel way to learn linear principal component analysis (PCA). Actually it is a weighted PCA and leads to a semi-definite optimization problem (SDP). In this paper, we learn linear and nonlinear PCA with linear programming problems, which are easy to be solved and can obtain the unique global solution. Moreover, two algorithms for learning linear and nonlinear PCA are constructed, and all principal components can be obtained. To verify the performance of the proposed method, a series of experiments on artificial datasets and UCI benchmark datasets are accomplished. Simulation results demonstrate that the proposed method can compete with or outperform the standard PCA and kernel PCA (KPCA) in generalization ability but with much less memory and time consuming.     

线性动态系统的对偶性环

这篇文章探讨了在哪类交换环上使线性动态系统的对偶原理成立,得到了交换环是线性动态系统的对偶性环的充分与必要条件。     

基于非线性观测器的离散驱动混沌同步

1　引言混沌同步是通过驱动信号的作用使得受迫系统的状态与驱动系统趋于一致.在系统与控制领域有一个相关问题就是通过系统的观测信号来估计该系统的状态,即“观测器”问题.混沌作为一类特殊的非线性动力系统,很自然地可引入观测器理论更系统地进行同步设计,且能用于同步方法所不能实现的某些系统中[1].混沌同步的一个主要应用方面是保密通信,而一般的同步方法均采用时间连续驱动信号,在数字通信占主流的今天,时间离散驱动的同步系统能够提供更高的频谱效率和保密性能[2,3],本文对基于观测器的混沌同步的条件进行分析,并导出了离散驱动时混…     

Induced Convolution Operator Norms of Linear Dynamical Systems

In this paper we develop explicit formulas for induced convolution operator norms and their bounds. These results generalize established induced operator norms for linear dynamical systems with various classes of input–output signal pairs. Date received: April 1, 1999. Date revised: February 21, 2000.     

非线性系统迭代学习算法

对于一个未知的非线性连续系统或离散系统,从任给的一个初始控制出发,尝试实现一条给定的输出目标轨线.在满足一定条件下,利用跟踪误差来修正控制函数,经过反复的迭代学习可以取得满意的效果.本文改进了Arimoto、Togai和Bien等的开环迭代学习的收敛条件,并提出闭环迭代学习算法.理论与仿真结果证明了闭环算法在收敛条件、速度和抗干扰能力上都优于开环算法.     

非线性系统高阶迭代学习算法

结合迭代学习控制算法中的开环和闭环方案，本文针对更一般的非线性系统，讨论高阶算法的广泛适用性。理论和仿真结果表明了高阶算法在输出跟踪和干扰抑制方面的有效性。     

基于线性可逆性变换的混沌同步控制

基于线性可逆性变换方法,提出一种提高变量耦合控制混沌同步有效性的方案．通过将系统的部分状态变量在相应的子空间做线性可逆性变换,增强系统状态变量之间的关联,从而用单一变量信号实现了对整个混沌系统的同步控制．以洛伦兹系统为例,仿真模拟了这种方案的有效性．     

非线性动力系统混沌现象的仿真实验

基于 Visual Basic6.0编制了非线性动力方程计算机仿真实验软件 ,通过对达芬 (Duffing)方程产生混沌现象的实例仿真分析 ,可动态观察到出现混沌现象时的轨线图、庞加莱 (Poincarè)映射图、振动时程曲线图和幅频图等。     

Switching Linear Dynamical Systems for Noise Robust Speech Recognition

Real world applications such as hands-free dialling in cars may have to deal with potentially very noisy environments. Existing state-of-the-art solutions to this problem use feature-based HMMs, with a preprocessing stage to clean the noisy signal. However, the effect that raw signal noise has on the induced HMM features is poorly understood, and limits the performance of the HMM system. An alternative to feature-based HMMs is to model the raw signal, which has the potential advantage that including an explicit noise model is straightforward. Here we jointly model the dynamics of both the raw speech signal and the noise, using a switching linear dynamical system (SLDS). The new model was tested on isolated digit utterances corrupted by Gaussian noise. Contrary to the autoregressive HMM and its derivatives, which provides a model of uncorrupted raw speech, the SLDS is comparatively noise robust and also significantly outperforms a state-of-the-art feature-based HMM. The computational complexity of the SLDS scales exponentially with the length of the time series. To counter this we use expectation correction which provides a stable and accurate linear-time approximation for this important class of models, aiding their further application in acoustic modeling.     

On Hankel Singular Values and Reflected Zeros of Linear Dynamical Systems

This note discusses a relationship between the Hankel singular values and reflected zeros of linear systems. Our main result proves that the Hankel singular values of a linear continuous-time system increase (decrease) pointwise when one or more zeros of the transfer function are reflected with respect to the imaginary axis, that is, move from the left-(right-)half to the right-(left-)half of the complex plane. We also derive a similar result for linear discrete-time systems.      

Evolutionary Adaptation of Nonlinear Dynamical Systems in Computational Neuroscience

We propose evolutionary analysis by synthesis as a powerful tool in computational neuroscience. We present applications of evolution strategies to the adaptation of dynamical systems for brain modeling. First, we compare evolutionary and gradient-based optimization of dynamic neural fields on an artificial benchmark problem. Then we adjust a few-neuron model developed for explaining our recent findings in a neurobiological experiment, in which we studied the processing of temporal sequences of stimuli in the cortex.     

An Invariance Principle for Nonlinear Discrete Autonomous Dynamical Systems

This note proposes an extension of LaSalle's invariance principle for nonlinear discrete autonomous dynamical systems. The invariance principle is extended to allow the first difference of the auxiliar scalar function (usually a Lyapunov function) to be positive in some bounded regions. Moreover, a uniform version is proposed to deal with nonlinear discrete dynamical systems that vary with parameters. Both extensions have the original invariance principle as a particular case. As a consequence, a larger class of systems can be treated with this new theory. The extensions are very useful to obtain attractor estimates as well as their corresponding stability regions. The uniform version, in particular, is useful to obtain estimates that are uniform regarding parameters     

基于线性控制的一类金融系统的混沌同步

研究了一类金融混沌系统的同步问题,给出了同步金融混沌系统的三种线性控制方案。仅使用简单的线性控制器就实现了全局渐近同步,因此可看作是已有结果的改进。在第一种方案中,利用李雅普诺夫稳定性理论,使用线性反馈控制得到了同步两个金融混沌系统的充分条件,后两种方案通过数值方法得到了同步条件。数值仿真结果说明了文中所给方法的有效性。     

自组织前向神经网络与非线性动态系统模化

将自组织学习过程引入到前向网络的训练中,提出了一种新的三层前向神经网络的训练方法,训练过程首先利用自组织分族算法确定隐含层结点的数目以及权值,然后通过求解线性最小二乘问题估计输出层权值,自组织过程产生的激活权值对输入数据具有一种特征变换的功能,利用该方法训练的网络可以称之为自组织前向网络（ＳＯＦＮ）。文中通过实际非线性动态系统建模的例子,说明了ＳＯＦＮ网络具有良好性能。