Study on Optimality of Two-Stage Estimation with ARMA Model Random Bias

1.INTaoDUCTIONInrecentyearsconsiderableworkhasbeendoneontheproblemofestimatingthestateofalinearsystemwitharandombiasthatinfluencesthesystemdynamicsandobservations.Thebasicmethodistheaugmelltedstateestimationwhosecomputationincreaseswiththebiajsvectordimension.Tomailltaincomputationalamountatalevel,theideaofusingatwasstagestateestimationtoimplementaugmentedstateestimationisintroducedbyFreidland[1],whichistodecouplethecentralfilterintotwoparallelfilters.Thefirstfilter,the"biasfree"filter,isb…     

Power control scheme for multiple antenna systems with space-time coding in Rayleigh fading channels

Two optimal power control(PC) schemes under the power constraint for space-time coded multiple input multiple output systems over the flat Rayleigh fading channel with the imperfect channel state information(CSI) are presented.One is based on the minimization of a bit error rate(BER),and the other is based on the maximization of a fuzzy signal-to-noise ratio.In these schemes,different powers are allocated to individual transmit antennas rather than equal power in the conventional one.For the first scheme,the optimal PC procedure is developed.It is shown that the Lagrange multiplier for the constrained optimization in the power control does exist and is unique.A practical iterative algorithm based on Newton’s method for finding the Lagrange multiplier is proposed.In the second scheme,some existing schemes are included,and a suboptimal PC procedure is developed by means of the asymptotic performance analysis.With this suboptimal scheme,a simple PC calculation formula is provided,and thus the calculation of the PC will be straightforward.Moreover,the suboptimal scheme has the BER performance close to the optimal scheme.Simulation results show that the two PC schemes can provide BER lower than the equal PC and antenna selection scheme under the imperfect CSI.     

Self-tuning measurement fusion white noise deconvolution estimator with correlated noises

For the multisensor linear discrete time-invariant stochastic systems with correlated noises and unknown noise statistics, an on-line noise statistics estimator is presented by using the correlation method. Substituting it into the steady-state Riccati equation, the self-tuning Riccati equation is obtained. Using the Kalman filtering method, based on the self-tuning Riccati equation, a self-tuning weighted measurement fusion white noise deconvolution estimator is presented. By the dynamic error system analysis (DESA) method, it is proved that the self-tuning fusion white noise deconvolution estimator converges to the optimal fusion steadystate white noise deconvolution estimator in a realization, so that it has the asymptotic global optimality. A simulation example for Bernoulli-Gaussian input white noise shows its effectiveness.     

两段卡尔曼估值器及最优条件研究

考虑了具有ARMA模型随机偏差的两段卡尔曼估值器的最优条件问题。首先给出了增广状态的最优卡尔曼滤波和两段卡尔曼估值器 ;其次证明了在一定的代数约束条件下 ,两段卡尔曼估值器和增广状态的最优卡尔曼滤波是等价的 ;最后 ,由于给定的代数约束条件在实际系统中是受限制的 ,因此结论表明两段卡尔曼估值器是次优的。     

Sensor selection for random field estimation in wireless sensor networks

This paper studies the sensor selection problem for random field estimation in wireless sensor networks.The authors first prove that selecting a set of l sensors that minimize the estimation error under the D-optimal criterion is NP-complete.The authors propose an iterative algorithm to pursue a suboptimal solution.Furthermore,in order to improve the bandwidth and energy efficiency of the wireless sensor networks,the authors propose a best linear unbiased estimator for a Gaussian random field with quantized measurements and study the corresponding sensor selection problem.In the case of unknown covariance matrix,the authors propose an estimator for the covariance matrix using measurements and also analyze the sensitivity of this estimator.Simulation results show the good performance of the proposed algorithms.     

易逝品随机生产库存模型动态定价、服务水平和生产控制策略

本文研究需求受价格和服务水平双重影响下的易逝品随机生产库存模型,探讨考虑外部随机扰动对库存变动影响下易逝品企业的最优联合动态定价、服务和生产策略,并基于随机最优控制理论,运用Hamilton-Jacobi-Bellman(HJB)方程对最优策略进行了求解.研究表明:最优动态价格、服务水平和生产速率是库存水平的线性反馈形式;外部随机扰动的大小对易逝品生产企业所获得的折现利润总期望会产生不同影响,在整个经营周期内外界不确定因素越大,易逝品生产企业所获得的折现利润总期望越小;价格敏感系数和服务敏感系数会影响易逝品企业生产、服务、价格策略.     

On optimal mean-field control problem of mean-field forward-backward stochastic system with jumps under partial information

This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When the coefficients of the system and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. The authors also investigate the mean-field type optimal control problem for the system driven by mean-field type forward-backward stochastic differential equations (FBSDEs in short) with jumps, where the coefficients contain not only the state process but also its expectation under partially observed information. The maximum principle is established using convex variational technique. An example is given to illustrate the obtained results.     

求解随机规划问题新方法——优劣解法

随机规划最优化,即使随机规划的目标函数最优化,达到最优值。那么怎样求随机规划目标函数的最优值呢?设随机规划问题min z=c′x,C为n维随机列向量,x为n维列向量,D为约束域。求其在满足约束条件下随机目标函数的最优值z~*=c′x~*。而如何判断随机变量是最小的呢?下面就此讨论,从而提出比较随机变量的方法。     

Markov 跳变系统输出峰值控制

针对具有时间演化和事件驱动两类动态机制的Markov线性跳变系统,研究其被控输出的峰值控制问题,当系统外部输入能量有界时,保证系统输出的峰值在给定的上限内.从工程实现的角度,利用随机稳定性分析,以一种次优的峰值指标代替最优性能,反馈控制器的构造依赖于系统模态,可直接利用耦合线性矩阵不等式求解.仿真示例对结果进行了验证,并对比讨论了应用鲁棒控制思想的控制器设计情形,说明模态跳变转移信息对系统指标与控制的影响.     

Optimal Output Tracking Control and Stabilization of Networked Control Systems with Packet Losses

This paper studies the optimal output tracking control and stabilization for networked control systems with packet losses via output feedback control. Both finite-horizon and infinite-horizon cases are considered. For the finite-horizon case, the authors introduce an augmented system according to the state variable and the reference trajectory for the first time. Based on a set of difference Riccati equations, an optimal output feedback tracking controller is proposed by applying the stochastic maximum principle. And an optimal estimator is presented. For the infinite-horizon case, a necessary and sufficient condition for the stabilization of the system is provided. And an optimal output feedback stabilizing tracking controller is obtained by establishing a set of algebraic Riccati equations. Finally,numerical examples are given to verify the proposed results.     

随机弹性需求条件下基于CVaR与收益共享契约的供应链决策模型

在条件风险估值的风险度量准则下, 建立了随机弹性需求条件下基于收益共享契约的供应链决策模型, 分析了集权供应链系统以及分权供应链系统中风险规避零售商与风险规避供应商的最优决策行为, 并进一步探讨了随机需求变量服从均匀分布时集权与分权供应链系统的最优决策.研究结果表明集权供应链系统的最优库存因子随整个供应链风险规避度的减小而减小, 而整个供应链的风险规避度对最优销售价格的影响则与随机需求变量的分布函数有关.分权供应链系统中的最优库存因子则仅与零售商的风险规避度有关, 而最优零售价格受零售商的风险规避度、收益共享系数和批发价格等因素的共同影响.另外, 研究还发现分权供应链系统的最优收益共享系数受各成员企业的风险规避度的影响, 即零售商越害怕风险或供应商越不害怕风险, 分权供应链系统的最优收益共享系数则越大.但数值分析结果却表明在绝大多数情形下收益共享契约机制并不能完美协调此类分权供应链系统.     

多态退化串联可修系统的最优维修更换策略

针对工程技术领域中的多失效状态的串联退化可修系统, 提出了一种维修更换模型. 假设系统中的部件有多个失效状态, 故障时以一定的概率进入其中某个状态, 部件不能修复如新. 以系统中部件的故障次数为更换策略, 系统的平均费用率为目标函数, 利用推广的几何过程理论建立数学模型, 证明了最优维修更换策略的存在性. 最后, 通过一个数值例子验证了本方法的有效性.     

一类随机摄动系统的最优控制与仿真

在内模控制(IMC)结构下对控制能量存在约束时一类随机摄动系统的最优控制及其仿真方法作了探讨。首先在鲁棒重新设计的基础上,针对一类随机模型误差的描述提出了一个平均意义上的包含跟踪误差和控制能量的性能指标,然后通过谱分解极小化该性能指标导出一个最优的内模控制器设计方法,可以兼顾模型摄动和控制能量约束,最后根据随机摄动系统的特点进行仿真研究进一步说明了所得控制方法的有效性。     

短期降雨预测的随机微分模型

在Nakita等的确定型短期降雨预测模型的基础上，利用随机微分方程理论。给出了预测降雨强度的随机模型．通过随机分析理论，求出了随机模型的解，同时研究了求解的近似数值方法和利用Fourier变换转化该随机降雨模型方程为常微分方程组的可行性．最后把文章提出的随机波动模型和NAk．klta提出的确定型短期预测模型运用到Nakita 1996年给出的降雨事件中进行预测和比较，效果良好．     

Solution to stochastic LQR problem with multiple inputs

This paper considers the stochastic linear quadratic regulation(LQR) problem for It stochastic systems with multiple input controllers. The explicit controllers are given in terms of two Riccati equations by introducing one new costate and establishing the homogeneous relationship between the state and the new costate. More importantly, it is more computation saving for the derived Riccati equations than the one derived by augmentation technique.     

一个批处理机随机E/ T 调度问题研究

对批处理机随机E/T(earliness and tardiness)调度问题,假设各批的加工时间独立同分布;各工件的交付期相互独立,并与加工时间独立;目标是极小化所有工件的提前与延迟时间和的均值.在加工时间和工件的交付期都服从指数分布的条件下,得到了最优调度的几个性质,基于这些性质用动态规划给出了一个求问题最优解的算法,此算法的时间复杂度为O(n2B2)(B相似文献   

Maximum principle for forward-backward stochastic control system with random jumps and applications to finance

<正> Both necessary and sufficient maximum principles for optimal control of stochastic systemwith random jumps consisting of forward and backward state variables are proved.The control variableis allowed to enter both diffusion and jump coefficients.The result is applied to a mean-varianceportfolio selection mixed with a recursive utility functional optimization problem.Explicit expressionof the optimal portfolio selection strategy is obtained in the state feedback form.     

Test on Stochastic Block Model: Local Smoothing and Extreme Value Theory

In this paper, to obtain a consistent estimator of the number of communities, the authors present a new sequential testing procedure, based on the locally smoothed adjacency matrix and the extreme value theory. Under the null hypothesis, the test statistic converges to the type I extreme value distribution, and otherwise, it explodes fast and the divergence rate could even reach n in the strong signal case where n is the size of the network, guaranteeing high detection power. This method is simple to use and serves as an alternative approach to the novel one in Lei (2016) using random matrix theory. To detect the change of the community structure, the authors also propose a two-sample test for the stochastic block model with two observed adjacency matrices. Simulation studies justify the theory. The authors apply the proposed method to the political blog data set and find reasonable group structures.

     

Stochastic differential equations and stochastic linear quadratic optimal control problem with Lévy processes

In this paper, the authors first study two kinds of stochastic differential equations (SDEs) with Lévy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimensional backward stochastic differential equations (BSDEs) driven by Lévy processes, the authors proceed to study a stochastic linear quadratic (LQ) optimal control problem with a Lévy process, where the cost weighting matrices of the state and control are allowed to be indefinite. One kind of new stochastic Riccati equation that involves equality and inequality constraints is derived from the idea of square completion and its solvability is proved to be sufficient for the well-posedness and the existence of optimal control which can be of either state feedback or open-loop form of the LQ problems. Moreover, the authors obtain the existence and uniqueness of the solution to the Riccati equation for some special cases. Finally, two examples are presented to illustrate these theoretical results. This work was supported by the National Basic Research Program of China (973 Program) under Grant No. 2007CB814904, the Natural Science Foundation of China under Grant No. 10671112 and Shandong Province under Grant No. Z2006A01, and Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20060422018.     

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.