A New Method of State Estimation for Singular Discrete-time Stochastic Linear System

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带状随机线性系统状态的估计问题

针对目前关于广义系统状态估计的研究现状 ,即几乎所有的讨论都集中在奇异矩阵为方阵的情况 ,讨论了广义逆矩阵和矩阵的奇异值分解问题。首次提出了带状随机系统的状态估计问题 ,利用矩阵的奇异分解理论给出了带状广义连续线性系统的奇异值标准形式。基于标准形式 ,利用广义逆矩阵的性质 ,在两种情况下将系统分解成两个子系统 ,通过估计子系统的状态 ,得到了该系统状态的最优预测和滤波递推方程。     

广义连续随机线性系统的最优递推问题

讨论了广义连续随机线性系统的最优递推问题,利用矩阵的奇异值分解理论,给出了广义连续随机线性系统的奇异值标准形式,基于标准形式,在两种情况下,将系统分解成两个子系统,通过对子系统状态估计的研究,得到了该系统的最优递推方程。结果表明,对于广义系统,该方法有效地减少了计算量。     

A New Approach to Optimal Filtering for SingularDiscrete-Time Stochastic Linear System

1IntroductionBecausetherealisticproblemwhichsingularsystemdescribesiswiderthanthenormalsystemsdo,theresearchofsingularsystemshasreceivedagreatdealofattention.Andmanyachievementshavebeenobtainedinthefieldsofstructuralcharacteranalysisanddesignmethodsofsingularsystems.Butforthestateestimationonlypreliminaryprobehasbeenmade.References[2]--[51proposedrespectivesolutionsbasedonleastsquaremethod.References[6]--[71transformsingularsystemsintonormalsystemsthroughmatrixresolutionandthenmakeuseofKalman…     

非线性离散动态大系统的DISOPE关联预测递阶算法

提出了一种非线性离散动态大系统系统优化与参数估计集成的关联预测递阶算法 .在各子系统模型与实际存在差异的情况下 ,将动态系统系统优化与参数估计集成 ( DISOPE)方法与关联预测法相结合 ,得到一个上级协调 ,下级进行各子系统优化与参数估计集成的双环迭代算法 ,从模型出发通过迭代运算能得到实际系统在存在模型 -实际差异时的真实最优解 .仿真结果表明了算法的有效性和实用性.     

Closed-Loop Iterative Learning Control for Discrete Singular Systems with Fixed Initial Shift

This paper deals with the problem of iterative learning control for a class of discrete singular systems with fixed initial shift. According to the characteristics of the discrete singular systems, a closed-loop learning algorithm is proposed and the corresponding state limiting trajectory is presented.It is shown that the algorithm can guarantee that the system state converges uniformly to the state limiting trajectory on the whole time interval. Then the initial rectifying strategy is introduced to the discrete singular systems for eliminating the effect of the fixed initial shift. Under the action of the initial rectifying strategy, the system state can converge to the desired state trajectory within the pre-specified finite time interval no matter what value the fixed initial shift takes. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.     

离散广义双线性系统的稳定控制分析

讨论了离散广义双线性系统稳定控制问题。研究了离散广义双线性系统稳定控制存在的条件,并给出了相应的控制方案。所采用的方法是利用广义系统分解,运用Lyapunov方法证明线性状态控制可以使闭环系统在原点附近渐近稳定。同时研究了不分解系统,通过构造广义李雅普诺夫函数的方法,给出了使闭环系统稳定的条件。对于离散广义双线性系统有关理论的证明,可以看作是正常离散双线性系统的拓广。     

混杂系统粒子滤波混合状态估计及故障诊断算法

混杂系统同时包含连续动态特性和离散动态特性,并且两种动态相互作用,使其故障诊断变得更加困难。针对此问题,提出了一种混合系统粒子滤波混合状态估计及故障诊断算法,提高了现有方法的适用范围和诊断效率。针对混杂系统受控迁移、自治迁移和随机迁移等特点,首先利用随机混杂自动机对系统离散状态(包括故障)和连续状态进行统一建模,重点对现有基于扩展卡尔曼粒子滤波的连续估计算法进行改进,支持利用在线监测数据来估计混杂系统各类迁移产生的各种离散和连续状态,最后根据离散状态估计结果快速实现故障诊断。通过对典型非线性混杂系统的故障诊断,证明了该方法的有效性。     

Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay

To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems,the Takagi-Sugeno(T-S)fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay.Based on the linear matrix inequality(LMI)techniques and stability theory of stochastic differential equations,a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller.The resulting closed-loop fuzzy system is robustly reliable stochastically stable,and the corresponding quadratic cost function is guarauteed to be no more than a certain upper bound for all admissible uncertainties,as well as different actuator fault cases.A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented.Finally,a numerical simulation is given to illustrate the effectiveness of the proposed method.     

Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay

To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.     

多种资源受限多项目排序问题的两层决策方法

分析了多种资源受限多项目排序问题的性质和特点 ,提出用两层决策方法建立这类问题的数学模型 .将基于直接搜索法的随机全局优化方法用于求解该问题的全局最优解 ,给出了具体的算法步骤 .计算示例表明 ,本文建立的模型和给出的算法能有效地求解多种资源受限多项目排序问题.     

A Maximum Principle for Fully Coupled Forward-Backward Stochastic Control System Driven by Lvy Process with Terminal State Constraints

This paper is concerned with a fully coupled forward-backward stochastic optimal control problem where the controlled system is driven by L′evy process, while the forward state is constrained in a convex set at the terminal time. The authors use an equivalent backward formulation to deal with the terminal state constraint, and then obtain a stochastic maximum principle by Ekeland's variational principle. Finally, the result is applied to the utility optimization problem in a financial market.     

一类不确定离散切换广义系统的一致有限时间稳定准则

利用Lyapunov like函数方法和线性矩阵不等式（linear matrix inequality, LMI）技术研究了一类不确定离散时间切换广义系统的一致有限时间稳定和状态反馈镇定问题。首先,在任意给定的切换规则且假定不确定参数项范数有界的情况下,给出了保证不确定离散切换广义系统一致有限时间有界和有限时间稳定的充分条件和状态反馈控制器的设计方法,然后利用Matlab中的LMI工具箱对建立的LMI问题进行求解。最后的仿真算例验证了所提方法的有效性。     

Bayesian estimation for nonlinear stochastic hybrid systems with state dependent transitions

The Bayesian approach is considered as the most general formulation of the state estimation for dynamic systems.However,most of the existing Bayesian estimators of stochastic hybrid systems only focus on the Markov jump system,few literature is related to the estimation problem of nonlinear stochastic hybrid systems with state dependent transitions.According to this problem,a new methodology which relaxes quite a restrictive assumption that the mode transition process must satisfy Markov properties is proposed.In this method,a general approach is presented to model the state dependent transitions,the state and output spaces are discreted into cell space which handles the nonlinearities and computationally intensive problem offline.Then maximum a posterior estimation is obtained by using the Bayesian theory.The efficacy of the estimator is illustrated by a simulated example.     

Nuclear Norm Subspace System Identification and Its Application on a Stochastic Model of Plague

The discrete-time model of plague is deduced by zero-order holder based on the continuoustime model. Due to the existence of stochastic disturbances, the stochastic model is given corresponding to the discrete-time model. The state estimation and noise reduction of the stochastic model are achieved by designing Kalman filter. Nuclear norm minimization is to structure the low-rank matrix approximation instead of the singular value decomposition in the process of subspace system identification. According to the plague data from the World Health Organization, the system matrices and noise intensity of the model are identified. Simulations are carried out to show the higher approximation capability of the proposed method.     

基于作业成本的产品组合决策随机模型与求解

通过引入生产作业系统的随机因素和市场需求的随机因素,基于作业成本系统,建立了考虑随机生产和随机需求的产品组合决策模型.使用确定性等价类和二阶段方法,将随机规划模型转化为确定性等价优化模型,避免了通过随机模拟进行求解的时间消耗.     

基于状态相关模态切换混合估计的航迹预测

针对航空器飞行轨迹预测的随机线性混杂系统估计问题,提出一种状态相关模态切换的混合估计算法(SDTHE). 该算法不仅解决了标准交互式多模型(IMM)算法似然函数为零均值高斯函数假设的缺陷,而且基于实时状态更新模态转移矩阵,使得飞行模态估计更为准确,从而提高飞行轨迹预测的精度. 与标准交互式多模型算法相比,仿真结果表明了所提出算法的有效性和优越性.     

离散广义大系统的渐近稳定与镇定

广义大系统的渐近稳定与镇定问题是广义大系统理论的基本问题之一 ,在许多领域均有广泛的应用。广义大系统的研究与广义系统相比困难得多。利用广义Lyapunov函数方法研究了离散广义大系统的渐近稳定与镇定问题 ,给出了渐近稳定的判定定理 ,设计了适当的反馈律 ,以实现离散广义大系统的镇定。该方法简单、直观 ,给出的例子说明了该定理的可行性。     

不确定系统鲁棒稳态白噪声反卷积平滑器

对于带不确定噪声方差的线性离散时不变随机系统,根据极大极小鲁棒估计原理,基于带噪声方差保守上界的最坏情形保守系统,应用Kalman滤波和最优白噪声估计理论,提出了一种鲁棒稳态白噪声反卷积平滑器。对于所有容许的不确定噪声方差,保证它的实际平滑误差方差阵有一个最小上界。基于Lyapunov方程方法证明了它的鲁棒性和鲁棒精度关系。一个数值仿真例子验证了所提出结果的正确性和有效性。     

认知雷达中基于Q学习的自适应波形选择算法

自适应波形选择器是认知雷达中智能发射器的重要组成部分。有效的波形选择能够在不同的环境下选择发射最优的波形序列,从而以更高的精度追踪目标。针对雷达目标转移概率未知这一特点,把自适应波形选择问题建模为随机动态规划模型,提出应用Q学习的方法来解决这个问题。仿真结果说明,该算法接近于最优波形选择方案,并且状态估计的不确定性低于固定波形。