Control for a Class of Stochastic Mechanical Systems Based on the Discrete-Time Approximate Observer

This paper investigates the observer-based control problem of a class of stochastic mechanical systems. The system is modelled as a continuous-time It o stochastic differential equation with a discrete-time output. Euler-Maruyama approximation is used to design the discrete-time approximate observer, and an observer-based feedback controller is derived such that the closed-loop nonlinear system is exponentially stable in the mean-square sense. Also, the authors analyze the convergence of observer error when the discrete-time approximate observer servers as a state observer for the exact system. Finally, a simulation example is used to demonstrate the effectiveness of the proposed method.     

Numerical Solutions for Optimal Control of Stochastic Kolmogorov Systems

This work is concerned with controlled stochastic Kolmogorov systems. Such systems have received much attention recently owing to the wide range of applications in biology and ecology.Starting with the basic premise that the underlying system has an optimal control, this paper is devoted to designing numerical methods for approximation. Different from the existing literature on numerical methods for stochastic controls, the Kolmogorov systems take values in the first quadrant. That is, each component of the state is nonnegative. The work is designing an appropriate discrete-time controlled Markov chain to be in line with(locally consistent) the controlled diffusion. The authors demonstrate that the Kushner and Dupuis Markov chain approximation method still works. Convergence of the numerical scheme is proved under suitable conditions.     

Bipartite Consensus of Discrete-Time Double-Integrator Multi-Agent Systems with Measurement Noise

The effects of measurement noise are investigated in the context of bipartite consensus of multi-agent systems. In the system setting, discrete-time double-integrator dynamics are assumed for the agent, and measurement noise is present for the agent receiving the state information from its neighbors. Time-varying stochastic bipartite consensus protocols are designed in order to lessen the harmful effects of the noise. Consequently, the state transition matrix of the closed-loop system is analyzed, and sufficient and necessary conditions for the proposed protocol to be a mean square bipartite consensus protocol are given with the help of linear transformation and algebraic graph theory. It is proven that the signed digraph to be structurally balanced and having a spanning tree are the weakest communication assumptions for ensuring bipartite consensus. In particular, the proposed protocol is a mean square bipartite average consensus one if the signed digraph is also weight balanced.     

White noise estimation for discrete-time systems with random delay and packet dropout

This paper is concerned with the optimal and suboptimal deconvolution problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal input white noise estimator is presented based on the stochastic Kahnan filtering theory. However, tb_e optimal white-noise estimator is timevarying, stochastic, and doesn＇t converge to a steady state in general. Then an alternative suboptimal input white-noise estimator with deterministic gains is developed under a new criteria. The estimator gain and its respective error covariance-matrix information are derived based on a new suboptimal state estimator. It can be shown that the suboptimal input white-noise estimator converges to a steady-state one under appropriate assumptions.     

Sampled-Data Stabilization of a Class of Stochastic Nonlinear Markov Switching System with Indistinguishable Modes Based on the Approximate Discrete-Time Models

This paper investigates the stabilization issue for a class of sampled-data nonlinear Markov switching system with indistinguishable modes. In order to handle indistinguishable modes, the authors reconstruct the original mode space by mode clustering method, forming a new merged Markov switching system. By specifying the difference between the Euler-Maruyama(EM) approximate discrete-time model of the merged system and the exact discrete-time model of the original Markov switching system, the authors prove that the sampled-data controller, designed for the merged system based on its EM approximation, can exponentially stabilize the original system in mean square sense. Finally, a numerical example is given to illustrate the effectiveness of the method.     

STOCHASTIC ADAPTIVE CONTROL FOR SYSTEMS WITH NOISE BEING AN ARMA PROCESS

Stochastic adaptive control is considered for the discrete-time multi-input and multi-output system of multi-delay with noise expressed by an ARMA process.The CARIMA model isa special case of the system in question.The optimal adaptive control law is given and it is shown thata quadratic cost function is minimized and the closed-loop system is stable.Further,when the systemis of minimum phase,the convergence rates of parameter estimates and of the cost-function are alsoderived.     

具有不确定性产出库存系统的随机比较

研究离散时间、单类产品、周期盘点的具有不确定性产出和不确定性需求库存系统的优化与设计问题,主要目的在于分析产出和需求的可变性对系统最优策略和最优费用的影响.对于单周期情形利用随机序的性质我们给出了最优库存水平和最优费用的随机比较结果.对于多周期具有独立产出率和独立需求的库存系统,利用动态规划方法证明了在一定的条件下最优库存水平关于时间具有随机单调性;对于多周期具有相关产出率和相关需求的库存系统,给出了系统最优费用的随机比较结果.     

离散时间修理延迟单部件可修系统的可靠性分析

针对离散时间下修理有延迟的单部件可修系统,建立了系统状态转移的数学模型。该模型假定系统有正常、维修和故障后待修三种状态,并且系统寿命、修复时间和等待修理时间均遵从一般离散分布。利用随机过程的方法,研究了该可修系统状态之间的转移关系。在该模型的基础上得到了系统可靠度、可用度、平均故障次数等常用可靠性指标。最后,通过一组算例来说明了该模型的有效性。     

基于自适应尺度变换-双稳态随机共振模型的BPSK信号检测算法

为提升在强噪声背景下对二进制相移键控(binary phase shift keying, BPSK)信号的检测性能, 针对主流方法在抑制噪声过程中信号受到一定程度的削弱、信号处理系统引入新噪声导致检测性能下降的问题,提出了基于自适应尺度变换双稳态随机共振模型的BPSK信号检测算法。对于经典的双稳态随机共振系统只能处理小幅度、低频段的周期信号的情况, 首先将双稳态随机共振系统进行尺度变换, 证明在高采样率条件下, 双稳态随机共振系统可应用于高频的BPSK信号, 并基于Neyman-Pearson准则设计了非线性阈值检测系统, 推导且定量表示出检测器的误码率, 以此作为反馈量, 自适应地调节系统参数, 构建了信号检测的完备流程。通过仿真实验验证了尺度变换的可行性以及所提算法的适用性, 为低信噪比条件下的弱BPSK信号检测提供了理论依据。     

A discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times

The authors discuss a discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times. As soon as the orbit is empty, the server takes a vacation. However, the server is allowed to take a maximum number J of vacations, if the system remains empty after the end of a vacation. If there is at least one customer in the orbit at the end of a vacation, the server begins to serve the new arrivals or the arriving customers from the orbit. For this model, the authors focus on the steady-state analysis for the considered queueing system. Firstly, the authors obtain the generating functions of the number of customers in the orbit and in the system. Then, the authors obtain the closed-form expressions of some performance measures of the system and also give a stochastic decomposition result for the system size. Besides, the relationship between this discrete-time model and the corresponding continuous-time model is also investigated. Finally, some numerical results are provided.     

On control of strong consensus for networked agents with noisy observations

The discrete-time first-order multi-agent networks with communication noises are under consideration.Based on the noisy observations,the consensus control is given for networks with both fixed and time-varying topologies.The states of agents in the resulting closed-loop network are updated by a stochastic approximation(SA) algorithm,and the consensus analysis for networks turns to be the convergence analysis for SA.For networks with fixed topologies,the proposed consensus control leads to consensus of agents with probability one if the graph associated with the network is connected.In the case of time-varying topologies,the similar results are derived if the graph is jointly connected in a fixed time period.Compared with existing results,the networks considered here are in a more general setting under weaker assumptions and the strong consensus is established by a simpler proof.     

ADAPTIVE STOCHASTIC APPROXIMATION FOR MEASUREMENT WITH CORRELATED NOISE

A multidimensional adaptive stochastic approximation procedure trun-cated at randomly varying bounds is studied for the regression function observedwith correlated noise.The algorithm is proved to be asymptotically efficient.Theresult of the paper generalizes the one shown in[1]for the observation noise be-ing i.i.d.random vectors and under other restrictive conditions imposed on theregression function.     

基于PH分布近似的系统维修优化模型研究

针对故障信息监测下的多状态劣化系统,建立了一类基于PH分布近似的视情维修优化模型,解决了同一模型中检测与预防性维修策略综合优化的问题.考虑到一般分布假设带来的建模与计算困难,提出了一类位相型(PH)分布近似方法,借助于PH分布良好的计算特性简化求解过程.由于该方法扩展了原有决策模型的状态空间,为了获得适用于原有模型假设条件的检测与维修优化策略,提出了一种改进的值迭代算法.运用该算法,可以确定系统最佳的预防性维修控制限和检测策略,保证其长期运行条件下的平均费用率最低.最后,通过具体算例验证了模型与迭代算法的可行性.     

社会养老保险中隐性债务的双随机模型

本文在利率与死亡率均为随机的背景下，对我国社会养老保险制度中的隐性债务进行分析．提出了两种方法，得到了养老金给付现值的期望值和方差，并对利率以Wiener过程建模，得到了期望值和方差的具体表达式．在实例中，采用Monte Carlo仿真的方法得到了养老金给付现值及其近似替代值的经验分布．     

一类模糊跳变系统的采样控制器设计

针对含有马尔可夫跳变参数的模糊系统,采用多李亚普诺夫函数方法,设计采样控制器,保证模糊跳变系统指数均方稳定和随机稳定。为便于工程应用,考虑到控制系统多为数字控制系统,计算机的输入、输出控制信号是数字信号,而被控对象常为连续时间系统,文中采用离散的控制器控制连续的被控对象。系统模型中的每个跳变模态对应的子系统均是T-S模糊系统,对每个模糊子系统采用平行分布补偿的控制方法,保证子系统渐近稳定。控制器的求解等效为线性矩阵不等式的可解性问题,便于求解。数值仿真结果验证了方法的可行性和有效性。     

数字闭环光纤陀螺建模与仿真研究

建立了数字闭环光纤陀螺的动态模型和随机模型。通过合理的近似,非线性动态模型简化为线性离散模型。设计了闭环数字控制算法,对光纤陀螺的动态响应进行了仿真。在随机建模中,运用不同的随机过程来模拟各种随机噪声,采用正交小波变换的方法来模拟1/f噪声,用白噪声一次离散积分的方法来模拟速率随机游走噪声,用一阶马尔可夫过程或指数相关随机序列来模拟指数相关噪声。进行了随机仿真,并用功率谱密度和Allan方差分析的方法对随机模型和仿真结果的有效性进行了验证。     

DIVERGENCE RATE OF STATE OF AR SYSTEMS WITH UNSTABLE UNIT ROOTS

The order of weighted sum of noise sequence for stochastic system is estimated by using limit theory in probability. Then the divergence rates of state of unstable AR system driven by noise of martingale difference sequence are established.     

基于容积卡尔曼滤波的约束恒模波束形成算法

提出一种基于容积卡尔曼滤波的线性约束恒模波束形成算法。首先使用伪观测法将恒模代价函数和约束条件写成状态观测方程,之后利用容积卡尔曼滤波算法来求解以上非线性滤波问题。所提方法能够避免常规算法对模型的近似处理和特征值分散效应对波束形成器输出性能的影响,因此对干扰和噪声有更强的抑制能力。仿真结果表明,本算法相比随机梯度法和递归最小二乘法具有更快的收敛速度和更高的输出信干噪比,在非平稳环境下,能够迅速调整权值收敛到最优解。     

Robust H∞ filtering for discrete-time systems with Markovian switching and time-delays

The robust H∞ filtering problem for uncertain discrete-time Markovian jump linear systems with modedependent time-delays is investigated. Attention is focused on designing a Markovian jump linear filter that ensures robust stochastic stability while achieving a prescribed H∞ performance level of the resulting filtering error system, for all admissible uncertainties. The key features of the approach include the introduction of a new type of stochastic Lyapunov functional and some free weighting matrix variables. Sufficient conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities. Numerical examples are provided to demonstrate the reduced conservatism of the proposed approach.     

规避资产重组金融风险的鲁棒H_∞控制策略研究

将资产重组过程中收益率的随机性通过其不确定性摄动和系统的不确定性扰动输入来体现 ,建立了资产重组问题的离散时间系统模型 ,基于时变离散系统 H∞ 优化设计思想 ,求得资本运营过程中能够确保资产财富按预期目标增值 ,有效抑制和防范金融风险的鲁棒 H∞ 控制策略 ,并通过一算例说明了算法的有效性