双稳随机共振系统信号调制噪声效应用于弱信号检测

通过对双稳系统随机共振模型的数值分析，得出在双稳系统输出信号中，有一个正弦信号成分和一个表现为维纳过程的噪声成分分别与输入的正弦信号和白噪声相对应。通过选择合适的系统参数，可以减小系统输出中信号和噪声之间的耦合效应。该系统可以大大抑制噪声，并在双稳系统中产生信号调制噪声效应。然后对双稳系统的输出信号作功率谱分析。不但可以辨识出淹没在白噪声中的微弱正弦信号的频率，还可以较精确地估算出微弱正弦信号的幅值。数值仿真表明，双稳系统的信号调制噪声效应可用于多个微弱正弦信号的检测。     

The equivalent discrete-time optimal control problem for time-varying continuous-time systems with white stochastic parameters

The transformation into discrete-time equivalents of digital optimal control problems, involving continuous-time linear systems with white stochastic parameters, and quadratic integral criteria, is considered. The system parameters have time-varying statistics. The observations available at the sampling instants are in general nonlinear and corrupted by discrete-time noise. The equivalent discrete-time system has white stochastic parameters. Expressions are derived for the first and second moment of these parameters and for the parameters of the equivalent discrete-time sum criterion, which are explicit in the parameters and statistics of the original digital optimal control problem. A numerical algorithm to compute these expressions is presented. For each sampling interval, the algorithm computes the expressions recursively, forward in time, using successive equidistant evaluations of the matrices which determine the original digital optimal control problem. The algorithm is illustrated with three examples. If the observations at the sampling instants are linear and corrupted by multiplicative and/or additive discrete-time white noise, then, using recent results, full and reduced-order controllers that solve the equivalent discrete-time optimal control problem can be computed.     

Optimal ensemble control of stochastic time-varying linear systems

We consider the optimal guidance of an ensemble of independent, structurally identical, finite-dimensional stochastic linear systems with variation in system parameters between initial and target states of interest by applying a common control function without the use of feedback. Our exploration of such ensemble control systems is motivated by practical control design problems in which variation in system parameters and stochastic effects must be compensated for when state feedback is unavailable, such as in pulse design for nuclear magnetic resonance spectroscopy and imaging. In this paper, we extend the notion of ensemble control to stochastic linear systems with additive noise and jumps, which we model using white Gaussian noise and Poisson counters, respectively, and investigate the optimal steering problem. In our main result, we prove that the minimum norm solution to a Fredholm integral equation of the first kind provides the optimal control that simultaneously minimizes the mean square error (MSE) and the error in the mean of the terminal state. The optimal controls are generated numerically for several example ensemble control problems, and Monte Carlo simulations are used to illustrate their performance. This work has immediate applications to the control of dynamical systems with parameter dispersion or uncertainty that are subject to additive noise, which are of interest in quantum control, neuroscience, and sensorless robotic manipulation.     

基于时变盲混合高斯白噪声干扰的卫星姿态随机自学习控制

本文提出一种基于统计模式识别,针对盲混合高斯白噪声干扰下卫星姿态控制的方法.通过对噪声样本进行数据挖掘和模式识别,在线学习噪声的实时特性,获得其概率密度函数的先验知识,应用此先验知识进行样本聚类、分类、无监督学习并对噪声参数进行精确估计.学习系统将干扰白噪声参数的精确估计值传送至随机最优控制器以获得精度优良的控制效果,通过仿真研究表明了方法的有效性.     

Self-tuning weighted measurement fusion white noise deconvolution estimator and its convergence analysis

White noise deconvolution or input white noise estimation has a wide range of applications including oil seismic exploration, communication, signal processing, and state estimation. For the multisensor linear discrete time-invariant stochastic systems with correlated measurement noises, and with unknown ARMA model parameters and noise statistics, the on-line AR model parameter estimator based on the Recursive Instrumental Variable (RIV) algorithm, the on-line MA model parameter estimator based on Gevers–Wouters algorithm and the on-line noise statistic estimator by using the correlation method are presented. Using the Kalman filtering method, a self-tuning weighted measurement fusion white noise deconvolution estimator is presented based on the self-tuning Riccati equation. It is proved that the self-tuning fusion white noise deconvolution estimator converges to the optimal fusion steady-state white noise deconvolution estimator in a realization by using the dynamic error system analysis (DESA) method, so that it has the asymptotic global optimality. The simulation example for a 3-sensor system with the Bernoulli–Gaussian input white noise shows its effectiveness.     

基于Kalman滤波的通用和统一的白噪声估计方法

用射影理论,基于Kalman滤波提出了通用和统一的白噪声估计方法,可统一解决带非零均值相关噪声的线性离散时变随机控制系统的白噪声滤波、平滑和预报问题.提出了输入白噪声估值器和观测白噪声估值器,最优和稳态白噪声估值器,固定点、固定滞后和固定区间白噪声平滑器,白噪声新息滤波器和Wiener滤波器.它可应用于石油地震勘探信号处理和状态估计,为解决信号和状态估计问题,提供了新的途径和工具.关于Bernoulli-Gaussian白噪声估值器的仿真例子说明了其有效性.     

Stochastic models for uncertain flexible systems

If a spectral operator is perturbed by an infinite-dimensional white noise process, it generates a stochastic evolution operator which has well defined second order properties. This type of stochastic bilinear spectral evolution equation may be used to model uncertainty of the higher modes in flexible systems. Three typical examples of flexible beams with bilinear white noise perturbations are analysed in detail and conditions are given for the existence of a steady state covariance operator.     

A stochastic system model of an educational institute

This paper is aimed at the development of a stochastic model for an academic institution. It is argued that many of the parameters of such an institute can only be effectively modelled in a probabilistic sense. It is proposed that all such parameters which cause a deterministic model of the institute to be erroneous can be lumped together as a white noise term in the state variable model. It is shown that the covariance of the noise term as well as the parameters of the deterministic part of the model can be recursively estimated on the basis of the known performance of the institute over a period of post several years. Once the model is identified it is shown that a prediction of the future performance of the institute is possible. The various concepts are illustrated in the paper on the basis of data collected from an existing institute.     

统一的快速次优固定区间白噪声Wiener平滑算法

对带相关噪声的线性离散随机控制系统,应用Kalman滤波方法,基于CARMA新息模型导出了统一的最优固定区间白噪声递推Wiener平滑器,它带有系数阵指数衰减到零的高阶多项式矩阵.进一步用截断方法提出了相应的快速次优固定区间自噪声Wiener平滑算法,它显著地减小了计算负担.给出了平滑误差公式和选择截断指数的公式.一个Bernoulli-Gaussian白噪声的仿真例子说明了所提出的结果的有效性.     

Conditions for the moment stability of linear stochastic systems

Sufficient conditions for the moment stability of linear differential stochastic equations with Ornstein-Uhlenbeck parameters are obtained on the base of moment stability theory with white noise parameters.     

Partial controllability of stochastic linear systems

The controllability concepts for linear stochastic differential equations, driven by different kinds of noise processes, can be reduced to the partial controllability concepts for the same systems, driven by correlated white noises. Based on this fact, in this article, we study the conditions of exact and approximate controllability for linear stochastic control systems under various kinds of noise processes, including correlated white noises as well as coloured, wide band and shifted white noises. It is proved that such systems are never exactly controllable while their approximate controllability is equivalent to the approximate controllability of the associated linear deterministic systems at all past time moments.     

Some properties of the dual adaptive stochastic control algorithm

The purpose of this paper is to compare analytically the properties of the suboptimal dual adaptive stochastic control with those of the optimal control, when plant dynamic contain multiplicative white noise parameters. A simple scalar example is used for this analysis.     

Combined identification of the input-output and noise dynamics of a closed-loop controlled linear system

The open-loop input—output dynamics and the noise dynamics of a feedback controlled linear system perturbed by coloured noise admitting a Markov representation are identified in state variable form using a two-stage algorithm. This system is equivalent to an augmented system driven by white noise.

First the input—output dynamics are identified through a stochastic approximation algorithm using superimposed white noise. Subtracting the model output from the system output yields correlated residuals which are then used to identify the noise dynamics using stochastic realization theory. An innovations representation is obtained that is equivalent to the above defined augmented system. The two stages are combined by a judicious coordinate transformation. The method can be applied on an operating feedback controlled process, regardless of the structure of the unknown suboptimal regulator.     

Updating response sensitivity models of nonlinear vibrating structures using particle filters

The problem of updating response gradients with respect to chosen system parameters based on spatially sparse measurements is considered. The measurement noise and imperfections in mathematical modeling are treated as Gaussian white noise processes. The system states are augmented by response gradients with respect to system parameters and an extended set of equations in the state space is formulated. These equations are cast in the form of Ito’s stochastic differential equations and measured data are assimilated into this model using Monte Carlo based Bayesian filtering tools. Illustrative examples include a few low dimensional dynamical systems with cubic and hereditary nonlinearities.     

Stochastic Resonance and Optimal Detection of Pulse Trains by Threshold Devices

The nonlinear detection by a threshold device of a periodic train of soliton-like pulses embedded in arbitrarily distributed white noise is studied. A theoretical model is developed which provides expressions for the signal-to-noise ratio at the output of the detector and for the input–output gain in signal-to-noise ratio. We analyze the properties and conditions of optimality for these quantities as functions of the parameters of the process. Especially, specific nonlinear properties not shared by linear devices are established, among which are the possibility of an input–output amplification of the signal-to-noise ratio and the demonstration that through nonlinear coupling the noise can be beneficial to the signal detection and that adding noise may result in improved performance via a mechanism known as stochastic resonance.     

Equivalent discrete optimal control problem for randomly sampled digital control systems

This paper considers the transformation of the optimal digital control problem to en equivalent discrete-time optimal control problem in the case of deterministic and stochastic sampling. The continuous-time system to be controlled is linear and disturbed by additive continuous-time white noise (not necessarily gaussian). The observations available at the sampling instants are in general non-linear and corrupted by discrete-time noise independent of the system noise (not necessarily additive, white or gaussian). The performance criterion is quadratic and an integral rather than a sum.     

Stochastic source seeking for nonholonomic unicycle

We apply the recently introduced method of stochastic extremum seeking to navigate a nonholonomic unicycle towards the maximum of an unknown, spatially distributed signal field, using only the measurement of the signal at the vehicle’s location but without the measurement of the vehicle’s position. Keeping the forward velocity constant and controlling only the angular velocity, we design a stochastic source seeking control law which employs excitation based on filtered white noise, rather than sinusoidal perturbations used in the existing work. We study stability with the help of stochastic averaging theorems that we recently developed for general nonlinear continuous-time systems with stochastic perturbations. We prove local exponential convergence, both almost surely and in probability, to a small neighborhood near the source. We characterize the convergence speed explicitly and provide design guidelines for maximizing it, as well as for minimizing the residual set near the source. We present a detailed simulation study, including a study of the effect of saturation on the steering input.     

Analytic expressions for rate and CV of a type I neuron driven by white gaussian noise

We study the one-dimensional normal form of a saddle-node system under the influence of additive gaussian white noise and a static "bias current" input parameter, a model that can be looked upon as the simplest version of a type I neuron with stochastic input. This is in contrast with the numerous studies devoted to the noise-driven leaky integrate-and-fire neuron. We focus on the firing rate and coefficient of variation (CV) of the interspike interval density, for which scaling relations with respect to the input parameter and noise intensity are derived. Quadrature formulas for rate and CV are numerically evaluated and compared to numerical simulations of the system and to various approximation formulas obtained in different limiting cases of the model. We also show that caution must be used to extend these results to the Theta neuron model with multiplicative gaussian white noise. The correspondence between the first passage time statistics for the saddle-node model and the Theta neuron model is obtained only in the Stratonovich interpretation of the stochastic Theta neuron model, while previous results have focused only on the Ito interpretation. The correct Stratonovich interpretation yields CVs that are still relatively high, although smaller than in the Ito interpretation; it also produces certain qualitative differences, especially at larger noise intensities. Our analysis provides useful relations for assessing the distance to threshold and the level of synaptic noise in real type I neurons from their firing statistics. We also briefly discuss the effect of finite boundaries (finite values of threshold and reset) on the firing statistics.     

Stabilisation of stochastic delayed systems with Lévy noise on networks via periodically intermittent control

ABSTRACT

This paper investigates the stabilisation of stochastic coupled systems with time-varying delays and Lévy noise on networks (SCSTLN) via periodically intermittent control. And here, internal delays, white noise and Lévy noise are considered in the networks. To ensure stability of SCSTLN with a periodically intermittent controller, several simple and useful criteria are obtained by establishing a new differential inequality and using a graph-theoretic approach. The intensity of control is closely related to the coupling strength and the perturbed intensity of white noise and Lévy noise. In particular, the stabilisation of stochastic coupled oscillators with time-varying delays and Lévy noise on a network as a practical application of our theoretical results is studied. Finally, a numerical example about oscillators network is carried out to show the validity and feasibility of our analytical results.