比例再保险问题的奇异型最优控制模型

在带有股利分配的比例再保险模型的基础上, 加入了债务和破产补偿因素, 建立了比例再保险问题中一类新的奇异型最优随机控制模型.利用随机分析的方法详尽分析了股利分配、债务和破产补偿因素对保险公司准备金的具体影响, 按收益率和偿债率的大小关系得出了不同情形下的最优控制策略及相应的最大收益的显式表达式.     

具有直接前馈控制的奇异分散系统的反馈控制

研究具有直接前馈的奇异分散系统。利用状态空间方法，我们导出了该系统通过静态输出反馈达到单通道Ｒ－可控与单通道Ｒ－可稳的条件。利用这些条件，我们研究了这类系统的分散极点配置问题与分散可稳性问题。本文的结果可用于研究带前馈的奇异摄动分散系统。     

基于奇异熵和随机森林的人脸识别

提出了一种基于奇异熵与随机森林的人脸识别方法。该方法以奇异熵来描述人脸特征。首先在整个人脸图上进行奇异值分解,应用整体奇异熵提取人脸全局特征。然后将人脸图像分成均匀子块,在各子块中进行奇异值分解,应用局部奇异熵提取人脸局部特征。之后将整体奇异熵和局部奇异熵融合形成最终分类特征。最后通过随机森林分类器对其进行分类。在Yale人脸库上的实验表明,该方法对表情、光照具有鲁棒性,且有较高的识别率和较短的识别时间。     

Buck型变换器非奇异固定时间滑模控制

针对存在参数不确定性的Buck变换器系统,提出一种非奇异固定时间滑模控制方法。首先,设计非奇异固定时间滑模面,并基于该滑模面设计固定时间控制器,保证系统输出电压误差在固定时间内收敛到平衡点的邻域内,且其收敛时间上界与系统初始状态无关。其次,设计自适应律估计系统不确定干扰上界,有效抑制不确定干扰对系统的影响,该方法无需干扰上界的先验知识。最后,仿真结果验证了所提方法的有效性。     

一类非线性随机系统的自适应控制

本文在文献「１，２」的基础上，对一类仿射非线性随机系统的最小二乘（ＬＳ）自适应控制问题进行了分析，给出了稳定性及收敛速度结果，在这里，我们仅要求非线性函数具有线性增长速度，而无需任何其它结构假设。     

具有时滞的奇异系统H∞控制

针对具有时滞的奇异系统H∞输出反馈控制问题,利用Lyapunov泛函方法,得到闭环系统稳定且具有H∞-范数界γ的充分条件,基于相应的LMI可行解给出了动态控制器显式表示.最后,数值例子表明了该方法的正确性.     

一类非线性不确定系统的非奇异Terminal滑模控制

针对一类二阶非线性系统提出新的Terminal滑模控制面以克服传统的Terminal滑模控制的奇异问题，同时确保系统从任何初始状态能在有限时间内收敛至平衡点．进一步考虑系统参数摄动和外界扰动等不确定性因素上界的未知性，用Lyapunov稳定性方法给出了一个带有未知性上界参数估计的自适应非奇异Terminal滑模控制（NTSM）控制．最后通过实例比较三种滑模控制方法，仿真结果验证了非奇异Terminal滑模控制能克服传统的Terminal滑模控制的奇异问题，并说明了自适应非奇异Terminal滑模控制的有效性和可行性．     

基于支持向量机的MEMS陀螺仪随机漂移补偿

针对传统方法的不足,将支持向量机应用于MEMS陀螺仪随机漂移的补偿。建立了支持向量机预测模型,通过相空间重构技术,将标量的随机漂移时间序列嵌入到一个辅助的相空间中进行模型的训练和测试,并使用最优化算法得到了核函数和预测模型的各项参数。训练和预测结果均表明,该方法具有很好的预测效果,是一种有效的MEMS陀螺仪随机漂移补偿方法。     

基于误差扩散和均值漂移的DSA特征点选择

数字减影血管造影（DSA）技术在血管疾病的诊断和治疗中起着重要的作用。在DSA图像配准算法中,控制点的精度、数量以及它们在图像上分布的情况在很大程度上决定了几何校正和配准的精度。控制点通常采用规则的网格点,然而更加有效的方法是利用图像本身的特征提取控制点。提出了一种基于误差扩散（Error Diffusion）和均值漂移（Mean Shift）的DSA特征点选择算法。该算法引入误差扩散是为了利用图像本身的特征自适应地选择控制点。在边缘和纹理复杂区域取较多控制点（网格密集）,相反在平坦区域取较少控制点。引入均值漂移的目的是为了减少控制点的数量。实验结果表明,该算法可以自适应地把控制点安排到血管等关键图像特征上,并可以根据需要对控制点的数量进行优化。     

三维半导体器件漂移扩散模型的并行有限元方法研究

本文设计了一种新的三维自适应迎风稳定化有限元方法(SUPG-IP),并对比研究了几种半导体器件模拟的并行有限元方法.数值模拟结果表明:稳定化有限元方法适用于大偏压以及高掺杂器件模拟;而经典的Zlamal有限元方法更适用于计算半导体器件的电学响应曲线.我们基于三维并行自适应有限元平台PHG开发了半导体器件漂移扩散模型求解器DevSim,并对几种典型的半导体器件进行了模拟测试.计算结果与商业软件Sentaurus吻合较好,验证了算法的有效性.我们对PN结进行了超大规模网格并行模拟测试,网格达8亿单元并使用2048进程计算,展示了算法良好的并行可扩展性.     

分数布朗运动干扰下广义随机系统滑模控制

本文考虑分数布朗运动干扰下时滞广义随机系统的基于观测器的滑模控制.首先设计了不受分数布朗运动干扰的状态观测器,然后给出了基于观测器的积分型滑模面函数的定义.为了研究观测器系统有限时间随机有界性,构造了带有二重积分的新型Lyapunov函数来处理分数布朗运动.利用奇异值分解原理,解决了观测器增益矩阵设计问题.利用线性矩阵...     

Deterministic and stochastic control of discrete-time bilinear systems

Optimal control of a class of time invariant single-input, discrete bilinear systems is investigated in this paper. Both deterministic and stochastic problems are considered.

In the deterministic problem, for the initial state in a certain set ∑₀, the solution is the same as the solution to the associated linear system. The optimal path may be a regular path or a singular path.

The stochastic control problem is considered with perfect state observation, and additive and multiplicative noise in the state equation. It is demonstrated that the presence of noise simplifies the analysis compared to that in the determinstic case.     

基于最小相关系数的扩散去噪的最优停止时间选取

讨论了图像去噪的扩散方程模型中所存在的最优停止时间选取问题。通过对图像点乘一个与梯度成反比的作用系数来构造一个新的去噪后的图像与去掉的噪声之间的相关系数,最优停止时间的选取就等价于极小化该相关系数。该准则能有效抑制图像中高频信息的存在对相关系数计算的影响,获得准确的最优停止时间,并无需预先知道图像中的噪声水平。仿真计算结果表明采用该准则所得的停止时间非常接近于基于最优峰值信噪比所得的停止时间,且广泛适用于各种噪声水平。     

Boundary control of stochastic reaction‐diffusion systems with Markovian switching

This article focuses on the boundary control of stochastic Markovian reaction‐diffusion systems (SMRDSs). Both the cases of completely known and partially unknown transition probabilities are taken into account. By using the Lyapunov functional method, a sufficient condition is obtained under the designed boundary controllers to guarantee the asymptotic mean square stability for SMRDSs with completely known transition probabilities. For the case of partially unknown transition probabilities, we introduce free‐connection weighting matrices to handle the boundary control problem. When external disturbance enters the system, a sufficient criterion of H‐infinity boundary control is developed. Furthermore, robust stabilization is investigated for parametric uncertain SMRDSs in both cases. Two examples are presented to demonstrate the efficiency of the proposed approaches.     

基于状态观测器的多面体不确定随机广义系统鲁棒预测控制

针对It?o型多面体不确定随机广义系统,提出一种离线观测器型鲁棒预测控制器的综合方法.通过构造带有误差项的增广随机Lyapunov函数,运用多维It?o公式和LMI方法,将“min-max”随机规划问题等价转化为一组线性矩阵不等式的求解问题;给出了控制器存在的充分条件和参数表达式,证明了初始时刻的可行解可以保证闭环广义系统的随机容许性.仿真算例验证了该方法的有效性.     

Singular optimal control for stochastic linear quadratic singular system using ant colony programming

In this article, singular optimal control for stochastic linear singular system with quadratic performance is obtained using ant colony programming (ACP). To obtain the optimal control, the solution of matrix Riccati differential equation is computed by solving differential algebraic equation using a novel and nontraditional ACP approach. The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution computed by the ACP approach to the problem is qualitatively better. The solution of this novel method is compared with the traditional Runge Kutta method. An illustrative numerical example is presented for the proposed method.     

Asymptotic stability in probability of singular stochastic systems with Markovian switchings

This paper investigates the problem of asymptotic stability in probability for singular stochastic systems with Markovian switchings. A stochastic Lyapunov theorem on asymptotic stability in probability for the considered systems is provided. Also, we show that the original system has the same stability property as its difference‐algebraic form based on singular value decomposition. By utilizing the earlier results, a sufficient condition is obtained in terms of linear matrix inequalities, which is easy to check by using standard software. Copyright © 2017 John Wiley & Sons, Ltd.     

Boundary control of linear stochastic reaction‐diffusion systems

This paper considers the boundary control problem for linear stochastic reaction‐diffusion systems with Neumann boundary conditions. First, when the full‐domain system states are accessible, a boundary control is designed, and a sufficient condition is established to ensure the mean‐square exponential stability of the resulting closed‐loop system. Next, when the full‐domain system states are not available, an observer‐based control is proposed such that the underlying closed‐loop system is stable. Furthermore, observer‐based controller is designed for the systems with an H_∞ performance. Simulation examples are given to demonstrate the effectiveness and potential of the new design techniques.     

Stability analysis of switched singular stochastic linear systems

ABSTRACT

This paper is devoted to study the stability of switched singular stochastic linear systems with both stable and unstable subsystems. By using the method of multiple Lyapunov functions and the notion of average dwell time, we provide sufficient conditions for the exponential mean-square stability of switched singular stochastic systems in terms of a proper switching rule and the linear matrix inequalities. An example is given to illustrate the effectiveness of the obtained results.     

Robust control for synchronization of singular complex delayed networks with stochastic switched coupling

This paper investigates the robust H _∞ control of synchronization for uncertain singular complex delayed networks with stochastic switched coupling. The switched coupling is dependent on a continuous time Markovian process. Based on Lyapunov–Krasovskii stability theory, sufficient conditions for the existence of the H _∞ control laws are given in terms of linear matrix inequalities, which ensure robustly global mean-square synchronization and a prescribed H _∞ disturbance attenuation level for the resulting closed-loop complex networks. Numerical examples are given to illustrate the effectiveness of the proposed method.