Stochastic direct integration schemes for dynamic systems subjected to random excitations

In this work, a stochastic version of direct integration schemes is constructed, based on a general recursive state space formulation. The technique is applicable to evaluating the second order response statistics of systems subjected to non-stationary random excitations, and is potentially able to handle non-proportional damping. A specific group of these algorithms obtained using one of the most frequently used families of time stepping schemes is introduced. It is shown that statistics obtained for two multi-degree of freedom (MDOF) dynamic systems using the proposed method are in close agreement with those obtained from Monte Carlo simulation when a proper time step is used. Stability of the proposed scheme is systematically investigated and it is concluded that, for the response statistics to be bounded, the time step used in the algorithm has to lie within certain limits.     

通过最佳控制解法确定隐含波动率

确定原生资产的隐含波动率无论是在理论还是实际应用上都有重要意义，本文利用Green函数法将此问题化为一个“终端”控制问题，通过最佳控制解法讨论了控制泛函极小元的存在性定理，并给出了极小元所满足的必要条件。     

Delay-dependent stability analysis for Markovian jump systems with interval time-varying-delays

This paper proposes improved stochastic stability conditions for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities (LMIs), less conservative delay-range-dependent stability conditions for Markovian jump systems are proposed by constructing a different Lyapunov-Krasovskii function. The resulting criteria have advantages over some previous ones in that they involve fewer matrix variables but have less conservatism. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper.     

电子鼻在小麦品质控制中的应用研究

采用PEN3型电子鼻系统对我国10个省份47个小麦样品的挥发性物质进行检测。通过Loadings分析不同传感器在模式识别中的贡献率,对传感器阵列进行优化,并对传感器的响应值进行了主成分分析(PCA)和线性判别分析(LDA)。结果表明W5S、W1S、W2S3根传感器在小麦样品的用途、产地、品种区分识别时作用都较大,W1C、W3C2根传感器贡献率较小。PCA分析可以区分面包用小麦和馒头面条用小麦,总贡献率达85.5%;也可以区分不同产地的小麦样品和同一产地不同品种的小麦样品。线性判别分析(LDA)仅可以对不同产地、不同品种的小麦样品实现部分区分,无法将不同用途的小麦区分开来。主成分分析效果优于线性判别分析。     

基于风险价值约束的动态均值-方差投资组合的研究

研究了基于风险价值约束的动态均值-方差项目投资组合的数学模型,该模型是控制带约束的随机线性二次型（LQ）控制问题.在讨论该随机LQ控制问题的解之后,给出投资组合动态数学模型对应的随机哈密顿-雅克比-贝尔曼方程的解,得出了有效边界和最佳策略,讨论了风险价值约束的影响.最后,针对某油田勘探开发项目的实际情况,应用上述结论求出该实例的解,并讨论了风险价值约束发挥的作用.     

虚拟控制增益函数未知的随机非线性系统模糊自适应控制

The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature. First, the so-called stochastic LaSalle theory is extended to some extent, and accordingly, the results of global ultimate boundedness for stochastic nonlinear systems are developed. Next, a new design scheme of fuzzy adaptive control is proposed. The advantage of it is that it does not require priori knowledge of virtual control gain function sign, which is usually demanded in many designs. At the same time, the track performance of closed-loop systems is improved by adaptive modifying the estimated error upper bound. By theoretical analysis, the signals of closed-loop systems are globally ultimately bounded in probability and the track error converges to a small residual set around the origin in 4th-power expectation.     

广义随机系统的集值滤波

在具有控制输入和动态噪声与观测噪声相关的情况下,给出线性随机系统的集值滤波方程;利用矩阵分解和系统变换的技巧,得到广义随机系统的集值滤波方程.这种状态估计方法适用于初始状态均值位于一个凸集之中的随机系统.与传统Kalman滤波产生单个条件分布不同,这里的集值滤波给出一个条件分布的凸集.     

乘性随机离散系统的最优控制

基于对系统随机不确定因素的分析,文中定义了一种新型随机离散系统--乘性随机离散系统,并研究该类系统的线性二次型(LQ)最优控制问题.首先给出了该类系统的有限时间和无限时间LQ最优控制律,并着重分析、证明了无限时间LQ最优控制问题的Riccati方程的正定矩阵解的存在性及相应数值求解算法与收敛性,以及闭环系统的稳定性等问题.仿真结果表明了该方法的有效性.     

基于均匀网格的Delaunay三角网算法在随机聚合网屏中的应用

Delaunay三角网一直是一个重要而有意义的研究课题,并具有极其广泛的用途。经过20多年来的研究,它的生成算法已趋于成熟。为了满足印刷、印染系统中随机聚合网屏生成的实时性需要,将一种将的算法引处到FM网屏技术中,并首先简要介绍了Delaunay三角网的牧场考及生成算法的分类;然后主要介绍了一种基于均匀网格的Delaunay三角网生成算法在随机聚合网屏中的应用;最后给出了算法的正确性证明。经测试,该算法的运算速度相当快,具有接近于线性的时间复杂性,能够满足排版印刷、印染系统中随机聚合网屏生成的需要。