On-line order estimation and parameter identification for linear stochastic feedback control systems (CARMA model)

This paper presents a new recursive estimate method for orders and coefficients of linear stochastic feedback control systems (CARMA model) under the assumption that the upper bounds of system orders are known. The strong consistency of the estimates for orders and coefficients is proved and the convergence rate of coefficient estimates to their true values is also obtained. The estimate algorithm is applied to adaptive tracking of the systems with unknown orders and unknown coefficients. The resulting closed-loop systems are then globally stable and the tracking sample mean square error is minimized as well. Simultaneously, the estimates of the adaptive tracking for orders and coefficients are also strongly consistent. The simulation results given here show that the new developed algorithms of both system identification and adaptive tracking are effective.     

Joint state and multi-innovation parameter estimation for time-delay linear systems and its convergence based on the Kalman filtering

This paper studies the joint state and parameter estimation problem for a linear state space system with time-delay. A multi-innovation gradient algorithm is developed based on the Kalman filtering principle. To improve the convergence rate, a filtering based multi-innovation gradient algorithm is proposed by using the filtering technique. The analysis indicates that the parameter estimates given by the proposed algorithms converge to their true values under the persistent excitation conditions. A simulation example is given to confirm that the proposed algorithms are effective.     

Computing non-fragile PI controllers for delay models of TCP/AQM networks

This article focuses on the stabilisation problem of fluid-flow delay models of transmission control protocol/active queue management (TCP/AQM) networks by using a proportional-integral (PI) controller as AQM strategy. More precisely, the complete set of PI controllers that exponentially stabilises the corresponding linear time-delay system is derived. Using the particular geometric properties of this set of the controller parameters, the issues of robustness to uncertainty in the network parameters and to perturbation in the controller coefficients are addressed. Then, a methodology to compute a non-fragile PI AQM controller is provided. Finally, exponential estimates for the closed-loop system solutions, allowing to evaluate the performance of the corresponding PI-controlled closed-loop system, are proposed by using a Lyapunov–Krasovskii functional approach. An illustrative example completes the presentation.     

时滞累积TDAGM($1,N,t)$模型及其在粮食生产中的应用

考虑到社会经济系统中广泛存在时滞因果关系,通过分析驱动因素对系统主行为的时滞累积作用效果以及系统行为线性发展趋势,构建了含时间趋势项的时滞累积型多变量灰色TDAGM($1,N,t$)模型,论证了GM(1, 1)、GM(1,N)、OGM(1,N)、时滞GM(1,N)、TDDGM(1,N)模型均是该模型在不同参数取值下的特殊形式;为避免模型求解过程中微分形式与差分形式转换而产生误差,通过定义TDAGM($1,N,t$)模型的派生形式,给出了TDAGM($1,N,t$)模型时间响应式的直接求解方法;针对模型时滞效应参数的识别和优化问题,基于粒子群优化算法,给出了TDAGM($1,N,t$)模型参数估计的算法框架.时滞系统的数值实验结果表明,TDAGM($1,N,t$)模型能够较好地解决含时滞特征的多变量系统预测问题.将该模型应用于河南省粮食产量预测的实例中,拟合精度较高且预测结果符合河南省粮食生产发展趋势,验证了模型的有效性.     

Analysis and parameter identification of time-delay linear systems via generalized orthogonal polynomials

A linear time-delay state equation is solved by the proposed generalized orthogonal polynomial (GOP) method. The parameter identification of such a system with time delay is also studied. The system is partitioned into several time intervals. Within a certain time interval, the state and control functions are assumed to be expressed by the GOP series. Time-delay differential equations are transformed into a series of algebraic equations of expansion coefficients. An effective algorithm is proposed to solve the time-delay system problem and to estimate the system parameters. By using such an effective computational algorithm, the calculation procedures are greatly simplified. Two illustrative examples are given to demonstrate the validity of the method. Very accurate results are obtained.     

An efficient hybrid reduction method for time-delay systems using Hermite expansions

This paper presents an efficient model reduction method for time-delay systems in the time domain. We expand the systems under a Hermite polynomial basis and show that Hermite coefficients of the expansion are determined by a linear equation, thus can be calculated efficiently. Such linear relationship is well taken in the projection methods of model reduction, and reduced models are generated to preserve a desired number of Hermite coefficients in the time domain, in contrast to other existing techniques which aim at approximating the transfer function of time-delay systems in the frequency domain. We also exploit two-sided projections for time-delay systems, leading to a hybrid reduction method which generates reduced models sharing the nice properties both in the time and frequency domains. Two numerical examples illustrate the feasibility and effectiveness of the approach.     

一类虚拟控制系数未知的随机非线性时滞大系统的适应镇定控制

研究了一类具有未知虚拟控制系数和未知噪声协方差的随机非线性时滞大系统的适应镇定问题. 首先, 针对系统的未知虚拟控制系数和未知噪声协方差, 选取了相应的估计参数; 然后, 针对时变时滞对闭环系统稳定性的影响, 构造了适当形式的Lyapunov-Krasovskii泛函, 采用积分反推方法给出了无记忆状态反馈控制律的系统设计过程. 在一定条件下, 证明了闭环系统平衡点依概率全局稳定, 且除参数估计以外的所有闭环信号几乎均收敛到零点. 仿真算例验证了所给方法的有效性.     

Serre’s reduction of linear partial differential systems with holonomic adjoints

Given a linear functional system (e.g., an ordinary/partial differential system, a differential time-delay system, a difference system), Serre’s reduction aims at finding an equivalent linear functional system which contains fewer equations and fewer unknowns. The purpose of this paper is to study Serre’s reduction of underdetermined linear systems of partial differential equations with either polynomial, formal power series or locally convergent power series coefficients, and with holonomic adjoints in the sense of algebraic analysis. We prove that these linear partial differential systems can be defined by means of only one linear partial differential equation. In the case of polynomial coefficients, we give an algorithm to compute the corresponding equation.     

Robust D-Stability Test of LTI General Fractional Order Control Systems

This work deals with the robust D-stability test of linear time-invariant(LTI) general fractional order control systems in a closed loop where the system and/or the controller may be of fractional order. The concept of general implies that the characteristic equation of the LTI closed loop control system may be of both commensurate and non-commensurate orders, both the coefficients and the orders of the characteristic equation may be nonlinear functions of uncertain parameters, and the coefficients may be complex numbers. Some new specific areas for the roots of the characteristic equation are found so that they reduce the computational burden of testing the robust D-stability. Based on the value set of the characteristic equation, a necessary and sufficient condition for testing the robust D-stability of these systems is derived. Moreover, in the case that the coefficients are linear functions of the uncertain parameters and the orders do not have any uncertainties, the condition is adjusted for further computational burden reduction. Various numerical examples are given to illustrate the merits of the achieved theorems.     

Monte Carlo evaluation of methods for pulse transfer function estimation

This paper describes the results of a Monte Carlo evaluation made of the methods proposed in current literature for the estimation of the pulse transfer function of a linear, time-invariant dynamic system with feedback. Considered are two basic methods for estimating the coefficients of a pulse transfer function, given only the normal operating input and output of the system obscured by noise and over a limited period of time. The most commonly proposed method is a linear method in which a set of simultaneous linear equations is formed from the sampled data and the coefficients obtained by a matrix inversion. The other method is an eigenvector method proposed by Levin which uses the eigenvector associated with the smallest eigenvalue of a matrix formed from the sampled data. This paper presents a set of examples designed to compare linear and eigenvector estimation methods and to verify experimentally the theoretical results and approximations given by Levin. The comparison shows that the eigenvector method generally gives estimates with equal or smaller rms errorsqrt{Variance+(Bias)^2}than the linear method. The eigenvector estimates had bias magnitudes which were consistently less than their standard deviations; the linear estimates did not, and thus had rms errors which often consisted largely of the bias. The approximate covariance matrix given by Levin for the coefficients estimated with the eigenvector method is found to be reasonably accurate.     

线性时滞中立型控制系统的滑动模补偿器方法

利用变结构控制理论，提出了线性不确定系数时滞中立型控制系统的一种新方法－－滑动模补偿器法。即当系统具有不确定系数时，引进一个滑动模补偿器，实现了完全的模型跟踪从而克服了用常规方法确定滑动曲面时所遇到的若干困难，为说明此法的设计技巧，给出了一个数值仿真例子。     

等间隔分数时延滤波器及其线性插值设计

针对宽带数字信号精确可变时延需求,研究等间隔分数时延滤波器及其线性插值方法。现有分数时延滤波器设计方法不能应用于可变时延,基于多采样率信号处理理论,提出等间隔分数时延滤波器设计方法。将所需时延近似为等间隔分数时延,选取对应时延滤波器组对信号进行时延,满足工程中变分数时延滤波需求。为提高时延滤波精度,提出对相邻滤波器系数线性插值的分数时延滤波器设计方法。对线性调频信号仿真结果表明,所提方法与常规分数时延滤波方法运算量相当,且适用于宽带信号的精确可变时延应用。     

Subspace-based identification of discrete time-delay system

We investigate the identification problems of a class of linear stochastic time-delay systems with unknown delayed states in this study. A time-delay system is expressed as a delay differential equation with a single delay in the state vector. We first derive an equivalent linear time-invariant (LTI) system for the time-delay system using a state augmentation technique. Then a conventional subspace identification method is used to estimate augmented system matrices and Kalman state sequences up to a similarity transformation. To obtain a state-space model for the time-delay system, an alternate convex search (ACS) algorithm is presented to find a similarity transformation that takes the identified augmented system back to a form so that the time-delay system can be recovered. Finally, we reconstruct the Kalman state sequences based on the similarity transformation. The time-delay system matrices under the same state-space basis can be recovered from the Kalman state sequences and input-output data by solving two least squares problems. Numerical examples are to show the effectiveness of the proposed method.     

线性奇异时滞系统的状态与不确定输入估计

研究了含不确定输入的线性奇异时滞系统的观测器设计.在一定秩条件下,通过引入 两个广义坐标变换,先将系统等价变换为不含不确定输入的正常状态空间时滞系统,再变换为 在系统描述中滞后项仅与输入和输出有关的系统.通过设计等价系统的状态观测器来获得原系 统的观测器,实现对原系统的状态与不确定输入的指数逼近.     

具有时滞的线性区间系统的鲁棒稳定性

本文给出了线性区间时滞系统鲁棒稳定性的一些结果，这些结果推广和改进了前人关于线性时滞系统鲁棒稳定性的相关结论，同时还讨论了线性区间时滞系统的稳定度，最后讨论了线性区间时滞大系统的鲁棒稳定性．     

具有时滞的线性区间系统的鲁棒稳定性

本文给出了线性区间时滞系统鲁棒稳定性的一些结果，这些结果推广和是了前人关于线性时滞系统鲁棒稳定性的相关结论，同时还讨论了线性区间时滞系统的稳定度，最后讨论了线性区间时滞大系统的鲁棒稳定性。     

Asymptotic properties of black-box identification of transfer functions

The problem of estimating the transfer function of a linear, stochastic system is considered. The transfer function is parametrized as a black box and no given order is chosen a priori. This means that the model orders may increase to infinity when the number of observed data tends to infinity. The consistency and convergence properties of the resulting transfer function estimates are investigated. Asymptotic expressions for the variances and distributions of these estimates are also derived for the case that the model orders increase. It is shown that the variance of the transfer function estimate at a certain frequency is asymptotically given by the noise-to-signal ratio at that frequency mulliplied by the model-order-to-number-of-data-points ratio.     

变时滞分布参数系统的全局指数稳定性

基于比较原理,利用推广的向量Hanalay微分不等式,Dini导数,结合Green公式及不等式分析技术,研究几类变时滞分布参数控制系统所导出的滑动模运动方程的全局指数稳定性问题,在仅要求系数矩阵是个M-矩阵的条件下,获得了几类滑动模运动方程全局指数稳定性的充分条件,建立了滑动模运动方程全局指数稳定性定理.推广和改进了前人的结论.并为研究时滞分布参数系统的变结构控制问题奠定了基础.     

具有时滞和干扰的多变量系统预测函数控制方法的研究

提出了一种新的多变量系统预测函数控制算法,该方法可以适用于具有时滞和外部干扰的多变量系统。利用该控制算法可得到一个解析的控制量计算方程,其中各个控制器参数均可离线计算,因此在线时算法简单,计算量小,可以广泛用于解决各种快、慢速对象的控制问题。仿真结果表明该多变量预测函数控制律具有克服干扰和时滞、跟踪性能好、控制精度高等特点。     

不确定线性时滞系统的稳定化控制器设计*

本文研究了不确定线性时滞系统的稳定化鲁棒控制器设计问题,给出了一类不确定线性时滞系统稳定化鲁棒控制器的设计方法,对于一般的不确定线性时滞系统,如果它们的标称系统是二次型能稳的,则该不确定线性时滞系统也是能稳的,且给出了其稳定化控制器的设计方法。