基于混沌理论的工业过程控制

通过改变系统李雅普诺夫指数对工业过程控制 中的混沌现象进行控制，并提出了一种确定控制区域的方法．理论分析和仿真实验结果表明 ，该控制策略是有效的，可以实现系统的快速稳定．     

基于 Lyapunov 指数的电力系统短期负荷预测

采用非线性系统理论对电力系统历史负荷数据序列进行了特征分析,计算出Ｌｙａｐｕｎｏｖ指数,并利用该Ｌｙａ－ｐｕｎｏｖ指数模式进行短期负荷预测,进而提出短期负荷预测的时间尺度的概念。这种方法不利用气候和气温等数据,只利用电力系统一维峰值负荷历史数据计算出过去的变动模式进行负荷预测,就可以得到较高的预测精度。对东北电网实际负荷数据进行了预测,结果令人满意,从而为电力系统短期负荷预测提供了一种新的预测方法。     

Modified mixture of experts employing eigenvector methods and Lyapunov exponents for analysis of electroencephalogram signals

Abstract: The use of diverse features in detecting variability of electroencephalogram (EEG) signals is presented. The classification accuracies of the modified mixture of experts (MME), which was trained on diverse features, were obtained. Eigenvector methods (Pisarenko, multiple signal classification – MUSIC, and minimum-norm) were selected to generate the power spectral density estimates. The features from the power spectral density estimates and Lyapunov exponents of the EEG signals were computed and statistical features were calculated to depict their distribution. The statistical features, which were used for obtaining the diverse features of the EEG signals, were then input into the implemented neural network models for training and testing purposes. The present study demonstrated that the MME trained on the diverse features achieved high accuracy rates (total classification accuracy of the MME is 98.33%).     

Stability and Chaos of a Class of Learning Algorithms for ICA Neural Networks

Independent component analysis (ICA) neural networks can estimate independent components from the mixed signal. The dynamical behavior of the learning algorithms for ICA neural networks is crucial to effectively apply these networks to practical applications. The paper presents the stability and chaotic dynamical behavior of a class of ICA learning algorithms with constant learning rates. Some invariant sets are obtained so that the non-divergence of these algorithms can be guaranteed. In these invariant sets, the stability and chaotic behaviors are analyzed. The conditions for stability and chaos are derived. Lyapunov exponents and bifurcation diagrams are presented to illustrate the existence of chaotic behavior.     

Which bases admit non-trivial shrinkage of formulae?

We show that the shrinkage exponent, under random restrictions, of formulae over a finite complete basis B of Boolean functions, is strictly greater than 1 if and only if all the functions in B are unate, i.e., monotone increasing or decreasing in each of their variables. As a consequence, we get non-linear lower bounds on the formula complexity of the parity function over any basis composed only of unate functions. Received: June 15, 2000.     

小波分析在检测探地回波奇异信号中的应用

本文基于Mallat的研究成果信号在突变点的奇异性表示（局部李氏指数）可以通过观测信号小波变换的模极大值随尺度变化的规律来刻画。将该理论应用到探地声波回波信号的处理中，通过追踪信号小波变换模极大值在不同尺度间的变化规律，来判断探地声波回波信号奇异点的位置，取得了较好的效果。     

Recurrent neural networks employing Lyapunov exponents for analysis of doppler ultrasound signals

The implementation of recurrent neural networks (RNNs) with the Lyapunov exponents for Doppler ultrasound signals classification is presented. This study is based on the consideration that Doppler ultrasound signals are chaotic signals. This consideration was tested successfully using the nonlinear dynamics tools, like the computation of Lyapunov exponents. Decision making was performed in two stages: computation of Lyapunov exponents as representative features of the Doppler ultrasound signals and classification using the RNNs trained on the extracted features. The present research demonstrated that the Lyapunov exponents are the features which well represent the Doppler ultrasound signals and the RNNs trained on these features achieved high classification accuracies.     

Robust control for a class of state-constrained high-order switched nonlinear systems with unstable subsystems

This paper addresses the issue of robust stabilisation for a class of state-constrained high-order switched nonlinear systems whose subsystems are allowed to be all unstabilizable. A novel robust control scheme is established based on effective coupling of the technique of adding a power integrator and the method of multiple barrier Lyapunov functions. Explicitly, a sufficient condition for robustly stabilising the resulting closed-loop system in a domain is presented, which meanwhile can also guarantee that the violation of the constraints does not happen. Moreover, in the switching law design, we do not require the connection of barrier Lyapunov functions for two adjacent subsystems, and even a certain amount of jump is also allowed. Finally, the effectiveness of the provided control strategy is demonstrated via a simulation example.     

网络环境下基于驻留概率信息的切换系统H_∞反馈控制

通过驻留概率信息的方法,研究了一类在网络环境下具有时变延迟的离散切换系统的H∞反馈控制问题.通过利用切换系统在每个子系统的驻留概率信息,将网络环境下的网络控制系统模型建模为一种新的切换系统模型.通过Lyapunov泛函方法,给出切换系统的H∞均方稳定的充分条件.然后,利用锥补线性化的方法得到控制器增益.最后,通过仿真算例验证所用方法的有效性.