Receding horizon H∞ control for discrete-time Markovian jump linear systems

Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality (LMI) form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

正态随机矩阵的MTP2性质

给出了正态随机矩阵的定义和一些相关性质,并将正态向量的多元全正二序(MTP2)性质的结论推广到正态随机矩阵.得到随机矩阵和它的任意行向量均满足MTP2的等价关系,以及正态随机样本矩阵为MTP2当且仅当总体的逆协方差阵为M-矩阵等结论.     

Ho∞-based fault detection for nonlinear networked systems with random packet dropout and probabilistic interval delay

The fault detection problem for the nonlinear networked control system (NCS) with packet dropout and delay is investigated.A nonlinear stochastic system model is proposed to account for the NCS with random packet dropout and networkinduced non-uniformly distributed time-varying delay in both from sensor to controller (S/C) and from controller to actuator (C/A).Based on the obtained NCS model,employing an observer-based fault detection filter as the residual generator,the addressed fault detection problem is converted into an auxiliary nonlinear H∞ control problem.Then,with the help of Lyapunov functional approach,a sufficient condition for the desired fault detection filter is constructed in terms of certain linear matrix inequalities,which depend on not only the delay interval but also the delay interval occurrence rate and successful packet communication rate.Especially,a trade-off phenomenon between the maximum allowable delay bound and successful data packet transmission rate is found,which is typically resulted from the limited bandwidth of communication networks.The effectiveness of the proposed method is demonstrated by a simulation example.     

一类带有栖息地偏好的生态系统模型

为了研究栖息地偏好对物种之间竞争结果的影响,从生物入侵的角度,建立了带有栖息地偏好的模拟生态模型,通过模拟讨论了该模型的性质,并研究了一类新问题,得到某一类物种个体的固定概率与另外一类物种个体固定概率的比值与第一类物种对第一种植物的偏好、第二类物种对第二种植物的偏好、第一种植物占所有植物的比例,以及前两类物种总数的关系,并且推导出前两类物种的个体的后代占据整个种群的概率公式,进一步利用Moran过程讨论,给出相应的计算过程。得出结论:生态系统受栖息地偏好的影响,该结果对研究栖息地偏好在物种竞争中的作用有一定的参考价值和指导意义。     

谱约束下拟反自反矩阵的最佳逼近问题

研究了拟反自反矩阵的逆特征值问题及其最佳逼近问题,建立了拟反自反矩阵逆特征值问题有解的充要条件,得到了解的表达式。进一步,对于任意给定的n阶复矩阵,得到了相关最佳逼近问题解得表达式。     

汽车二维碰撞模型的简便算法

为了对基于动量定理建立的汽车二维碰撞模型进行快速求解,利用矩阵分块处理原理建立了一种简便算法.通过矩阵分块处理可以降低所求模型的矩阵阶数,从而简化了求解过程.对典型汽车碰撞实例的分析表明:应用该方法能够迅速、准确地进行汽车碰撞事故的分析计算.     

一种圆柱壳体圆孔切割机构变胞特性分析

提出了一种新型的变胞切割机构,应用于机械设备尤其是舰艇圆柱壳体表面的孔切割.通过变胞切割机构的拓扑结构的变化,使机构自由度发生改变,以适应在切割过程中切割圆孔直口、在所开孔上切割变角度坡口,以及在直口切割和坡口切割之间进行切割状态转化的要求.在对其进行机构原理和2个构态下的自由度分析的基础上,应用拓扑结构图论和邻接矩阵分析了变胞切割机构在2个构态下的各个构件间的连接状态.建立了变胞方程和变胞矩阵,用以分析和描述整个变胞过程.理论分析结果说明了该机构的有效性和实用性。     

结合FDA与NMF的高光谱数据解混方法

高光谱图像解混是遥感图像处理的重要技术之一．利用非负矩阵分解（NMF）进行高光谱图像解混是近年来发展起来的一种方法．这种解混方法假设光谱具有稳定的光谱特性;但实际上光谱经常是多变的,这个现象影响着解混的精度．为了减小这一影响,首先利用Fisher判别分析（FDA）对高光谱数据进行线性变换,而后利用变换后的高光谱数据提出了一种FDA与NMF相结合的高光谱数据解混方法．实验表明新方法能够有效地提高解混精度与效率．     

具有混合时滞随机离散神经网络的渐近稳定性分析

研究了一类具有离散和分布时滞的随机离散神经网络的模型,通过构造新的Lyapunov-Krasovskii函数,给出了模型渐近稳定性的定理.以线性矩阵不等式形式给出的定理,易于用Matlab的LMI工具箱求解.最后通过仿真实例证明了定理的有效性.     

矩阵最小奇异值下界的一种估计

矩阵的奇异值是矩阵分析中的重要课题.其中矩阵奇异值的下界估计在许多领域中也是非常重要的,因此矩阵奇异值的下界估计得到了普遍的关注.对奇异值的下界做了进一步的研究,改进了黄廷祝的"矩阵最小奇异值下界的估计"一文的定理1以及定理2,并给出了相应的证明和数值算例.