On the Hankel-norm approximation of linear stochastic systems

We derive ordering and interlocking properties for the singular values of the block-Hankel matrices corresponding to different spectral factors of a given spectral density matrix. The results are then applied to Hankel-norm approximation of SISO stochastic systems. In particular we show that the minimum phase model may be approximated in Hankel norm by systems of a certain prescribed dimension with better accuracy than any other model with the same output process. We also provide upper bounds on the gain in accuracy obtained by choosing the minimum phase model over some other model.     

Variable structure control of stochastic systems

In this paper, the problem of variable structure control of stochastic (SVSC) systems is proposed and the corresponding variable structure control strategies with complete and incomplete state information are established. The concepts of stochastic sliding mode and sliding motion band are introduced which may be regarded as the basic characteristics of SVSC systems. Robustness of SVSC systems is considered and a general design procedure for SVSC systems is presented. The effectiveness of the proposed control method is shown by simulation results.     

Properties of optimal stochastic control systems with dead-time

Structural, stability and sensitivity properties of optimal stochastic control systems for dead-time, stable minimum phase as well as non-minimum phase processes are presented. The processes are described by rational transfer functions plus dead-times and the disturbances by rational spectral densities. It is shown that although the frequency domain design techniques guarantee asymptotically stable systems for given process and disturbance models, many of the designs might be practically unstable. Necessary and sufficient conditions that must be imposed on the design to assure practically stable optimal systems are derived. The uncertainties in the parameters and in the structure of the process model are measured by means of an ignorance function. Sufficient conditions in terms of the ignorance function, which guarantee stable design and by means of which the bounds of the uncertainties for a given design may be estimated, are stated. Conditions under which the optimal designs possess attractive relative stability properties, namely gain and phase margins of at least 2 and 60°, respectively, are stated, too. It is further shown that any optimal controller, for the type of processes discussed in this paper, may be separated into a primary controller and into a dead-time compensator where the latter is completely independent of the cost and the disturbance properties. Such a decomposition gives excellent insight into the role of the cost and the disturbance in the design. When low order process and disturbance models are used, the conventional PI and PID control laws coupled with the dead-time compensator emerge.     

Stochastic Distribution Control of Singular Systems: Output PDF Shaping

This paper presents a new algorithm designed to control the shape of the output probability density function (PDF) of singular systems subjected to non-Gaussian input. The aim is to select a control input uk such that the output PDF is made as close as possible to a given PDF. Based on the B-spline neural network approximation of the output PDF, the control algorithm is formulated by extending the developed PDF control strategies of non-singular systems to singular systems. It has been shown that under certain conditions the stability of the closed-loop system can be guaranteed. Simulation examples are given to show the effectiveness of the proposed control algorithm.     

一类随机系统完全统计特征控制

非线性随机系统完全统计特征控制优于低阶矩控制,但往往因为算法的复杂性难以实际应用.本文针对受高斯白噪声激励的标量非线性随机系统,针对状态响应提出了一种完全统计特征控制方法.首先将刻画完全统计特征的概率密度函数表示成指数函数,利用FPK(Fokker-Planck-Kolmogorov)方程求出概率密度函数的各阶导数,进而建立指数函数Taylor展开的系数与待求反馈控制增益间的关系.然后,依据控制目标给出了求解反馈增益的优化问题.针对目标概率密度函数的不同情况,分别给出了跟踪控制策略:对于指数函数Taylor展开为有限项形式的情况,能够直接得到控制增益并完全跟踪目标概率密度函数;其他情况下,也能够达到较好的控制效果.仿真验证了本文方法的有效性.     

On the adaptive control of a class of systems with random parameters and disturbances

The adaptive control of discrete time parameter linear stochastic systems with random parameters is investigated. It is shown that systems whose (unknown) autoregressive parameters undergo bounded martingale difference disturbances may be stabilized by the application of the so-called Modified Least Squares adaptive control algorithm. Asymptotically, the sample mean square performance criterion is equal to the one step ahead minimum variance control loss (which equals the prediction error variance when the system parameters are known) plus a term which is bounded by a quantity proportional to the square of the bound on the parameter disturbance. This latter term may be interpreted as the increase in the prediction error variance due to the random parameter variation.     

Frequency-domain identification of continuous-time ARMA models from sampled data

The subject of this paper is the direct identification of continuous-time autoregressive moving average (CARMA) models. The topic is viewed from the frequency domain perspective which then turns the reconstruction of the continuous-time power spectral density (CT-PSD) into a key issue. The first part of the paper therefore concerns the approximate estimation of the CT-PSD from uniformly sampled data under the assumption that the model has a certain relative degree. The approach has its point of origin in the frequency domain Whittle likelihood estimator. The discrete- or continuous-time spectral densities are estimated from equidistant samples of the output. For low sampling rates the discrete-time spectral density is modeled directly by its continuous-time spectral density using the Poisson summation formula. In the case of rapid sampling the continuous-time spectral density is estimated directly by modifying its discrete-time counterpart.     

Continuity of the spectral factorization on a vertical strip

The continuity of the mapping which associates a spectral factor to a spectral density is investigated. This mapping can be defined on several classes of spectral densities and spectral factors. For the usual largest class of spectral densities, i.e., essential bounded functions on the imaginary axis that are bounded away from zero, it is known that this mapping is not continuous. It is shown here that for slightly smaller, but still generic class the mapping becomes continuous.     

二值噪声激励下耦合欠阻尼双稳系统的随机共振

研究了二值噪声激励下耦合欠阻尼双稳系统的随机共振问题.首先,数值模拟二值噪声,研究了噪声参数对二值噪声输出的影响;其次,分析了噪声参数对系统输出的影响,发现随着噪声强度的增大,粒子可以在两个势阱之间进行跳跃,而且跳跃的频率随着噪声强度的增大而增大;最后,描述了噪声对系统输出功率谱以及信噪比的影响.结果发现在一定噪声强度下,功率谱的输出有峰的结构,并且峰值在关键的噪声处达到最大.特别地,对于不同的参数,信噪比的变化呈现非单调性,从而可以找到使信噪比峰值最大的最优参数.     

Identification of systems containing linear dynamic and static nonlinear elements

Identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered. Previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems. It is shown that systems composed of cascade, feedforward, feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only.     

Optimal instrumental-variable methods for identification of multivariable linear systems

The identification of multivariable linear systems using instrumental-variable (IV) methods is discussed. The emphasis is on accuracy properties. The IV estimates of multi-input-multi-output system parameters are proved to be asymptotically Gaussian distributed under weak conditions. An explicit expression for the covariance matrix of the parameter estimates is given. It is then shown how this matrix can be optimized by appropriately choosing the IV variant. The optimal accuracy so obtained is for some model structures equal to that corresponding to a prediction error method.     

Rational spectral factorization using state-space methods

We describe a state-space-based algorithm to find the minimum phase spectral factor of any rational spectral density, whether it be proper, improper, or polynomial.     

An ergodic AIMD algorithm with application to high-speed networks

In this article we propose a version of the Additive-Increase Multiplicative-Decrease (AIMD) algorithm that provides a suitable basis to develop congestion control protocols that can be deployed in both conventional and high-speed communication networks. Our algorithm retains many of the properties of the standard AIMD algorithm. However, unlike other non-standard AIMD algorithms, our scheme can be shown to be ergodic under very general assumptions.     

Identifiability of MIMO linear dynamic systems operating in closed loop

Identification of multi-input multi-output (MIMO) linear dynamic systems is considered for the case when the measurements are obtained during closed loop operation. Both noise free and noisy feedback situations are analysed. For the case where the disturbances in the feedback path are a full rank stochastic process it is shown that, under certain mild conditions, physically meaningful models for the forward and reverse paths can be uniquely determined. For the case where the feedback path is noise free it is shown that the forward path model can be uniquely determined provided the regulator satisfies certain minimal complexity requirements.     

Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle

In this paper, sampled-data based average-consensus control is considered for networks consisting of continuous-time first-order integrator agents in a noisy distributed communication environment. The impact of the sampling size and the number of network nodes on the system performances is analyzed. The control input of each agent can only use information measured at the sampling instants from its neighborhood rather than the complete continuous process, and the measurements of its neighbors’ states are corrupted by random noises. By probability limit theory and the property of graph Laplacian matrix, it is shown that for a connected network, the static mean square error between the individual state and the average of the initial states of all agents can be made arbitrarily small, provided the sampling size is sufficiently small. Furthermore, by properly choosing the consensus gains, almost sure consensus can be achieved. It is worth pointing out that an uncertainty principle of Gaussian networks is obtained, which implies that in the case of white Gaussian noises, no matter what the sampling size is, the product of the steady-state and transient performance indices is always equal to or larger than a constant depending on the noise intensity, network topology and the number of network nodes.     

基于ARMA的微惯性传感器随机误差建模方法

针对微惯性传感器随机误差建模效果不理想,影响微惯性组合导航系统性能的问题,提出了采用自回归滑动平均(ARMA)对微惯性传感器随机误差进行建模的方法。通过对随机误差模型应用于微惯性器件误差建模的深入分析,将Yule-Walker方程引入线性预测问题中,实现AR功率谱密度的估计,建立了基于随机过程有理功率谱密度的ARMA模型建立方法,并给出了ARMA建模准确性的LDA验证准则。通过微惯性传感器实测数据,对随机误差建模方法进行了有效性验证。该方法为微惯性器件的随机误差建模和分析提供了一种新的途径。     

多項式迭加平稳过程信号的預报过滤问題

本文考虑了系数未知的多项式迭加平稳过程的信号,给出了均方误差意义下最优预报及多项式系数估计公式中的谱特性应满足的必要和充分条件.当平稳过程具有有理谱密度时,可以把决定最优谱特性问题归结为解线性代数方程组.     

The role of the interactor matrix in multivariable stochastic adaptive control

This paper is concerned with the extension of the well-known minimum variance control strategy to the multi-input-multi-output case. It is shown that this extension is straightforward when the system interactor matrix is diagonal but presents some unexpected difficulties in the general case. We develop a suitable stochastic controller for the general case as a logical extension of the single input algorithm. We also explore the properties of the algorithm in detail. We also address the question of adaptive control of multivariable stochastic systems and investigate one possible strategy for overcoming the requirement of knowing the system interactor matrix a priori.     

Comments on: ‘Implementation of self-tuning regulators with variable forgetting factors’

The similarities are pointed out between the variable forgetting factor given in the paper by Fortescue, Kershenbaum and Ydstie and that given in Wellstead and Sanoff. Moreover, it is shown that the method of Fortescue, Kershenbaum and Ydstie can be made significantly more efficient, computationally, than is indicated.