On the hyperstability of a class of hybrid systems

Sufficient conditions of the hyperstability of a class of single-input single-output hybrid systems, composed of interconnected continuous and discrete subsystems, are given. Hyperstability is guaranteed by that of a discrete extended system which is built by incorporating samples of the continuous substrate. Asymptotic hyperstability is guaranteed by that of one discrete system, together with that of a continuous one. Both systems are related to an augmented state representation of the linear part of the overall system for all the nonlinear output-feedback time-varying actuators that satisfy generalized Popov-type inequalities.     

Hyperstability of linear time-varying discrete systems

The hyperstability of a class of linear time-varying discrete systems is studied. Sufficient conditions for hyperstability and for stability in the sense of Lyapunov are obtained.     

A result on the hyperstability of a class of hybrid dynamic systems

This paper presents a hyperstability theorem for a class of hybrid dynamic systems composed of coupled differential and difference equations subject to (possibly) time-varying nonlinearities satisfying a Popov-type inequality. The nonlinear controller generates the plant input at all times from its sampled values by defining an extended discrete system. The hyperstability results are obtained from this discrete system of special type whose state consists of the sampled continuous substate and the digital substate of the given hybrid system. Some corollaries and related physical interpretations are also given     

Identifiability of nonminimum phase linear stochastic systems

This paper considers the identifiability of time-invariant non-minimum phase systems for the ease of unobserved white Gaussian driving noise and no control input. It is shown that a sufficient condition for identifiability is that the driving noise should have a known time-varying perpetually exciting variance. Simulation results are given which support the theory.     

Noise variance estimation based on measured maximums of sampled subsets

In this paper, an estimation of the Gaussian noise variance based on observed (measured) maximums of subsets of samples is given. Circumstances of the measurement environment being limited, only maximums of subsets of samples are available and the non-constant variance of the Gaussian noise can be estimated. In the case of power line noise, the variance of the zero mean Gaussian noise is a periodic function of the a-priory known parameterization.Variance function parameters estimation is computed in two steps, first the estimation formula of the constant variance Gaussian noise is applied to a certain subset of samples and second, the least mean square (LMS) criterion is applied to fit the parametrized variance function to estimated variances.The maximum likelihood estimation (MLE) criterion is applied to derive estimators of the variance function parameters. Beside that, the quotient of the variance of the zero mean Gaussian noise and its maximums is evolved explicitly.Experimental results on real and simulated data are given to demonstrate their accuracy.     

Probabilistic solutions of some multi-degree-of-freedom nonlinear stochastic dynamical systems excited by filtered Gaussian white noise

In this paper, the state-space-split method is extended for the dimension reduction of some high-dimensional Fokker–Planck–Kolmogorov equations or the nonlinear stochastic dynamical systems in high dimensions subject to external excitation which is the filtered Gaussian white noise governed by the second order stochastic differential equation. The selection of sub state variables and then the dimension-reduction procedure for a class of nonlinear stochastic dynamical systems is given when the external excitation is the filtered Gaussian white noise. The stretched Euler–Bernoulli beam with hinge support at two ends, point-spring supports, and excited by uniformly distributed load being filtered Gaussian white noise governed by the second-order stochastic differential equation is analyzed and numerical results are presented. The results obtained with the presented procedure are compared with those obtained with the Monte Carlo simulation and equivalent linearization method to show the effectiveness and advantage of the state-space-split method and exponential polynomial closure method in analyzing the stationary probabilistic solutions of the multi-degree-of-freedom nonlinear stochastic dynamical systems excited by filtered Gaussian white noise.     

图像高斯噪声估计的极大似然算法

提出一种图像高斯噪声极大似然估计方法,目的是估计出噪声图像所含噪声大小。首先,根据高斯噪声模型的特点,用极大似然法估计噪声值,对图像所含噪声模型进行分析。其次,把噪声图像用直方图表示,从归一化直方图中选出不同的样本观测值,用极大似然算法对噪声的方差进行估计。最后,用MATLAB对该方法进行了模拟实验,实验结果表明此方法所得的图像噪声的方差与实际图像噪声的方差近似相等。所以,此方法无论是在准确性上还是在可行性上均具有优良的特性。     

具有方差和极点约束的不确定系统鲁棒H∞输出反馈控制

针对一类具有范数有界不确定性的连续系统和二次矩阵不等式区域,考虑系统具有方差和区域极点约束的输出反馈控制器设计问题．为此首先导出闭环系统区域稳定的充分必要条件．然后用线性矩阵不等式方法给出输出反馈控制器存在的一个充分条件．在此充分条件下闭环系统是鲁棒区域稳定的且具有H∞性能以及当干扰为白噪声信号时其稳态状态方差有限．接下来用矩阵分解方法给出输出反馈控制器增益矩阵的求解过程．最后通过一个仿真实例说明本文所提出的控制器设计方法的有效性．     

具有方差和极点约束的不确定系统鲁棒H∞输出反馈控制

针对一类具有范数有界不确定性的连续系统和二次矩阵不等式区域, 考虑系统具有方差和区域极点约束 的输出反馈控制器设计问题. 为此首先导出闭环系统区域稳定的充分必要条件. 然后用线性矩阵不等式方法给出输出反馈控制器存在的一个充分条件. 在此充分条件下闭环系统是鲁棒区域稳定的且具有H-infinity性能以及当干扰为白噪声信号时其稳态状态方差有限. 接下来用矩阵分解方法给出输出反馈控制器增益矩阵的求解过程. 最后通过一个仿真实例说明本文所提出的控制器设计方法的有效性.     

超稳定性方法及其在机器人控制中的应用

本文用超稳定性方法研究了一类以工业机器人为背景的模型參考自适应控制问题,克服了过去用超稳定性方法设计不能保证渐近稳定的缺点,并把该方法应用到工业机器人控制中.     

Gaussian mixture parameter estimation with known means and unknown class-dependent variances

This paper develops a recursive, convergent estimator for some parameters of Gaussian mixtures. The M class conditional (component) densities of the mixture random variable are Gaussian with known and distinct means and unknown and possibly different variances. A joint estimator of M prior (mixing) probabilities and M class conditional variances is derived. Sufficient conditions on the data and control parameters are derived for the estimator to converge. Convergence of the estimator follows from the use of a stochastic approximation theorem. Techniques to extend the estimators for the case of successive class labels forming a Markov chain are mentioned. The estimator has applications in blind parameter estimation in digital communication with symbol dependent noise variance and in image compression.     

State estimation by orthogonal expansion of probability distributions

A recursive estimation scheme suitable for real-time implementation is derived for a class of nolinear systems and observations expressed as nonlinear functions in discrete time, corrupted by a non-Gaussian mutually correlated random white noise sequence. The probability densities are expanded as a Gram-Charlier series and a Gauss-Hermite quadrature formula is used for computing the expectations. In the multidimensional case an expansion about a density of mutually independent Gaussian variables is used instead of a general multidimensional Gaussian density, which may result in a poorer performance in linear systems with Gaussian noise. However, in the case of nonlinear systems and non-Gaussian noise, the computational simplifications which result, outweigh the impairment in performance if any. A computational example is included.     

A Stochastic Kinematic Model of Class Averaging in Single-Particle Electron Microscopy

Single-particle electron microscopy is an experimental technique that is used to determine the 3D structure of biological macromolecules and the complexes that they form. In general, image processing techniques and reconstruction algorithms are applied to micrographs, which are two-dimensional (2D) images taken by electron microscopes. Each of these planar images can be thought of as a projection of the macromolecular structure of interest from an a priori unknown direction. A class is defined as a collection of projection images with a high degree of similarity, presumably resulting from taking projections along similar directions. In practice, micrographs are very noisy and those in each class are aligned and averaged in order to reduce the background noise. Errors in the alignment process are inevitable due to noise in the electron micrographs. This error results in blurry averaged images. In this paper, we investigate how blurring parameters are related to the properties of the background noise in the case when the alignment is achieved by matching the mass centers and the principal axes of the experimental images. We observe that the background noise in micrographs can be treated as Gaussian. Using the mean and variance of the background Gaussian noise, we derive equations for the mean and variance of translational and rotational misalignments in the class averaging process. This defines a Gaussian probability density on the Euclidean motion group of the plane. Our formulation is validated by convolving the derived blurring function representing the stochasticity of the image alignments with the underlying noiseless projection and comparing with the original blurry image.     

利用超稳定性理论证明随机自适应控制算法的稳定性

超稳定性理论是自适应控制稳定性证明的有力工具,但至今它只限于确定性系统.通过 对超稳定性理论进一步研究和算法结构变化,本文给出了利用超稳定性理论证明随机自适应 控制(特别是Goodwin的随机逼近法)的稳定性.结果表明,与目前的证明方法--Martingale 函数法和Ljurg的ODE法相比,超稳定性方法有相当的优越性.它不需要象Martingale 函数法那样去构造一个相当困难的随机Lyapunov函数,也可放松ODE法所必需的 系统噪声平稳的条件.     

Reliable H ∞ filter design for a class of mixed-delay Markovian jump systems with stochastic nonlinearities and multiplicative noises via delay-partitioning method

This paper is concerned with the problem of reliable H _?? filter design for a class of mixeddelay Markovian jump systems with stochastic nonlinearities and multiplicative noises. The mixed delays comprise both discrete time-varying delay and distributed delay. The stochastic nonlinearities in the form of statistical means cover several well-studied nonlinear functions. And the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. Furthermore, the failures of sensors are quantified by a variable varying in a given interval. A filter is designed to guarantee that the dynamics of the estimation error is asymptotically mean-square stable. Sufficient conditions for the existence of such a filter are obtained by using a new Lyapunov-Krasovskii functional and delaypartitioning method. Then a linear matrix inequality (LMI) approach for designing such a reliable H _?? filter is presented. Finally, the effectiveness of the proposed approach is demonstrated by a numerical example.     

基于统计假设测试的噪声方差估计方法

在数字图像处理中,噪声方差估计是一个重要的研究课题。提出一种针对加性高斯噪声的噪声方差估计方法。利用一种基于统计假设测试的方法来度量图像结构特征度,基于图像结构特征度找出平滑子块和非平滑子块（含有边缘或纹理子块）;以平滑子块中的最小方差为参考方差,选择出方差与参考方差相差在一定范围内且不含边缘的所有子块;从选出的子块中求以图像结构特征度为权重的方差平均值作为噪声方差估计值。相比于现有的噪声估计方法,该方法具有非常高的估计精度,适合感染高斯噪声的各种图像。     

Analysis of nonlinear stochastic systems by means of the Fokker–Planck equation†

Nonlinear systems disturbed by Gaussian white noises (or by signals obtained from Gaussian white noises) can sometimes be analysed by setting up and solving the Fokker–Planck equation for the probability density in state space. In the present paper a simplified derivation of the Fokker–Planck equation is given. The uniqueness of the steady-state solution is discussed. Steady-state solutions are obtained for certain classes of system. These solutions correspond to or slightly generalize the Maxwell–Boltzmann distribution which is well known in classical statistical mechanics     

On state variables filters for adaptive system design

An alternative way of using the state variable filters, coupled with the Kalman-Yacubovich lemma or Popov's hyperstability theorem, in the design of model reference adaptive systems is proposed. The improvement over previous designs is the increased flexibility in the selection of the filter parameters to reduce the effects of noise or initial conditions.     

A generalization of the hyperstability conditions for model reference adaptive systems

A generalization of the hyperstability criterion given in the literature is discussed. The new hyperstability conditions were obtained by utilizing the properties of the positive definite kernels. The results presented here are directly applicable for the synthesis of hyperstable adaptation algorithms for various applications.     

A new form of stable adaptive observer

A new form of adaptive observer which is guaranteed to be globally stable via hyperstability theories is presented. Its main advantage over existing designs is that asymptotic unbiased estimates are obtained in the presence of output noise. Experimental results are given to demonstrate the performance of this observer.