不确定非线性动力系统的稳定性分析

本文讨论渐近稳定的非线性名义动力系统在非线性时变扰动下的鲁棒稳定性问题。应用Ｌｙａｐｕｎｏｖ稳定性定理及其推广定理得出了非线性动力系统鲁棒稳定的若干判别准则，并给邮了应用所得准则的实际算例。     

基于H∞滤波的变权多通道数据融合方法研究

在对多通道定位数据进行数据融合中，采用H∞滤波可有效地解决各传感器数据误差模型不确定的滤波和状态估计问题。但由于数据采样时刻及精度的不一致性，对于多通道数据的融合应采用变权融合方式，以提高融合后数据的可靠性。该由此给出了一种基于H∞滤波的变权数据融合计算方法，通过对实测实时数据的仿真计算表明，其方法具有很好的实用性。     

Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties

The problem of robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties is investigated in this article. It is only assumed that the upper normal bound of uncertain inner and outer coupling matrices is positive but its concrete structure is not also required to be known. The time‐varying coupling delay is a any nonnegative continuous and bounded function and not require its derivative to be less than one, that is, general time‐varying coupling delays and uncertainties. For such a class of uncertain complex networks, a new synchronization scheme is presented by a class of continuous memoryless robust decentralized adaptive synchronization controllers. It is also shown that the synchronization error dynamics of uncertain complex networks can be guaranteed as uniformly exponentially convergent toward a ball that can be as small as desired. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of proposed complex networks synchronization schemes. © 2013 Wiley Periodicals, Inc. Complexity 19: 10–26, 2014     

Robust pair‐copula based forecasts of realized volatility

A useful application for copula functions is modeling the dynamics in the conditional moments of a time series. Using copulas, one can go beyond the traditional linear ARMA (p,q) modeling, which is solely based on the behavior of the autocorrelation function, and capture the entire dependence structure linking consecutive observations. This type of serial dependence is best represented by a canonical vine decomposition, and we illustrate this idea in the context of emerging stock markets, modeling linear and nonlinear temporal dependences of Brazilian series of realized volatilities. However, the analysis of intraday data collected from e‐markets poses some specific challenges. The large amount of real‐time information calls for heavy data manipulation, which may result in gross errors. Atypical points in high‐frequency intraday transaction prices may contaminate the series of daily realized volatilities, thus affecting classical statistical inference and leading to poor predictions. Therefore, in this paper, we propose to robustly estimate pair‐copula models using the weighted minimum distance and the weighted maximum likelihood estimates (WMLE). The excellent performance of these robust estimates for pair‐copula models are assessed through a comprehensive set of simulations, from which the WMLE emerged as the best option for members of the elliptical copula family. We evaluate and compare alternative volatility forecasts and show that the robustly estimated canonical vine‐based forecasts outperform the competitors. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust linear optimization under matrix completion

Linear programming models have been widely used in input-output analysis for analyzing the interdependence of industries in economics and in environmental science.In these applications,some of the entries of the coefficient matrix cannot be measured physically or there exists sampling errors.However,the coefficient matrix can often be low-rank.We characterize the robust counterpart of these types of linear programming problems with uncertainty set described by the nuclear norm.Simulations for the input-output analysis show that the new paradigm can be helpful.     

含非线性扰动的变时滞中立系统时滞相关稳定性新条件

研究一类含非线性扰动和混合时变时滞的中立型系统时滞相关鲁棒稳定性问题.通过构造包含三重积分项的Lyapunov-Krasovskii的泛函,结合积分不等式和自由权矩阵技术,建立了基于线性矩阵不等式(LMI)形式的离散时滞和中立时滞均相关的稳定性新判据.判据扩大了系统稳定所允许的最大时滞上界范围,具有更低的保守性.利用MATLAB的LMI工具箱进行了数值仿真,仿真算例验证了所提出的稳定性判据的有效性.     

基于改进自适应混沌控制的逆可靠度分析方法

自适应混沌控制方法是一种高效、稳健的逆可靠度分析方法,但在求解强非线性凹功能函数时,计算效率仍然有待提高,且可能会陷入局部最优.通过对混沌控制因子更新策略进行改进,提出了基于改进自适应混沌控制的逆可靠度分析方法.数值算例分析表明:该方法能够有效地改善混沌控制因子自适应选取时的合理性,具有更好的收敛性和更高的计算效率,为结构可靠度分析和可靠度优化问题提供了更加高效、稳健的求解途径.     

一类不确定时变时滞系统的鲁棒自适应稳定控制

研究了一类不确定时变时滞系统的鲁棒自适应稳定控制问题.系统包含多变时滞非线性扰动.基于Lyapunov稳定性理论和Lyapunov-K rasovsk ii型泛函设计出了一种无记忆的自适应状态反馈控制器,并证明了满足一定条件时,此控制器使得闭环系统最终一致有界.     

DELAY DEPENDENT ROBUST DISSIPATIVE CONTROL FOR A CLASS OF NONLINEAR TIME-DELAY SYSTEMS

We discuss the delay dependent robust dissipative problem for a class of time-delay systems with nonlinear perturbations. And the sufficient conditions for the delay dependent robust dissipation and quadratic stability are given by the linear matrix inequalities (LMIs), then the time-delay bound and the delay dependent robust dissipative state feedback controller are presented.     

General Robust-Optimization Formulation for Nonlinear Programming

Most research in robust optimization has been focused so far on inequality-only, convex conic programming with simple linear models for the uncertain parameters. Many practical optimization problems, however, are nonlinear and nonconvex. Even in linear programming, the coefficients may still be nonlinear functions of the uncertain parameters. In this paper, we propose robust formulations that extend the robust-optimization approach to a general nonlinear programming setting with parameter uncertainty involving both equality and inequality constraints. The proposed robust formulations are valid in a neighborhood of a given nominal parameter value and are robust to the first-order, thus suitable for applications where reasonable parameter estimations are available and uncertain variations are moderate. This work was supported in part by NSF Grant DMS-0405831