Comparison of the closed-loop identification methods in terms of the bias distribution

Several schemes for plant model identification in closed-loop operation including classical direct method, two-step identification and closed-loop output error algorithms are considered. These methods are analyzed and compared in terms of the bias distribution of the estimates for the case that the noise model is estimated as well as the case that a fixed model of noise is considered (output error structure). The problems concerning the filtered direct method which is often used in the iterative identification and control scheme are mentioned. It is shown that these problems may be solved by the closed-loop output error identification method.     

A cumulant based algorithm for the identification of input-output quadratic systems

The identification of a special class of polynomial models is pursued in this paper. In particular a parameter estimation algorithm is developed for the identification of an input-output quadratic model excited by a zero mean white Gaussian input and with the output corrupted by additive measurement noise. Input-output crosscumulants up to the fifth order are employed and the identification problem of the unknown model parameters is reduced to the solution of successive triangular linear systems of equations that are solved at each step of the algorithm. Simulation studies are carried out and the proposed methodology is compared with two least squares type identification algorithms, the output error method and a combination of the instrumental variables and the output error approach. The proposed cumulant based algorithm and the output error method are tested with real data produced by a robotic manipulator.     

Control oriented system identification: a worst-case/deterministicapproach in H∞

The authors formulate and solve two related control-oriented system identification problems for stable linear shift-invariant distributed parameter plants. In each of these problems the assumed a priori information is minimal, consisting only of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level. The first of these problems involves identification of a point sample of the plant frequency response from a noisy, finite, output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest. This problem leads naturally to the second problem, which involves identification of the plant transfer function in H_∞ from a finite number of noisy point samples of the plant frequency response. Concrete plans for identification algorithms are provided for each of these two problems     

Identifiability of linear stochastic systems operating under linear feedback

The identifiability of multiple input-multiple output stochastic systems operating in closed loop is considered for the case where the plant and the regulator are both linear and time-invariant. Two basic identification methods have been proposed for such systems: the joint input-output method, in which the input and output processes are modelled jointly as the output of a white noise driven system; and the direct method, in which a prediction error method is used on the input-output data as if the system were in open loop. Previously obtained identifiability results for the joint input-output method are extended to a number of new situations, including but extending beyond the identifiability results obtained with the direct method.     

基于子空间方法的精馏塔系统辨识建模研究

子空间辨识方法作为一种有效的针对多输入-多输出系统(MIMO)的辨识建模方法近年来受到广泛的重视.目前主要采用的子空间辨识算法只能适用于白噪声环境,而实际的工业现场数据很多是受到较大有色噪声干扰的.针对问题采用了一种新的子空间辨识算法,利用马尔可夫参数用于处理随机性部分,同时引入辅助变量用以去除噪声的干扰,能够适用于存在较大有色噪声干扰情况下的辨识建模,并可得到对象的无偏模型,建模的精度优于通常所采用的子空间辨识算法.通过对精馏塔仿真模型的辨识结果证明了该方法的可行性和有效性,以及在实际工业过程对象建模中良好的应用前景.     

基于虚拟参考反馈整定的改进无模型自适应控制

针对一类离散时间非线性系统, 提出一种基于虚拟参考反馈整定的改进无模型自适应控制方案. 首先, 利用动态线性化方法给出非线性系统的紧格式动态线性化模型; 然后, 基于优化技术设计控制算法和伪偏导数估计算法; 最后, 设计基于虚拟参考反馈整定的伪偏导数初值和重置值的估计算法. 该控制方案设计仅依赖于被控系统的输入和输出数据, 且能保证闭环系统的稳定性和收敛性. 仿真比较结果验证了所提出方法的有效性.

     

Suppression of “salt and pepper” noise based on Youden designs

This paper presents a new class of algorithms based on Youden designs to detect and restore edges present in an image imbedded by mixture or “salt and pepper” noise. The mixture noise consists of a uncorrelated or correlated noisy background plus uncorrelated impulsive noise. The objective is to restore pixels affected by the impulsive part of the mixture noise. The approach is to consider that these pixels have lost their true value and their estimate is obtained via the normal equation that yields the least sum of square error (LSSE). This procedure is known in the literature as “The Missing Value Approach Problem”. The estimates are introduced into the image data and an ANOVA technique based on Youden design is carried out. We introduce Youden designs which are special Symmetric Balanced Incomplete block (SBIB) designs, the pertinent statistical tests and estimates of the factor effects. We derive the estimate of the missing value for the uncorrelated noise environment as well as for the correlated one. The high level of performance of these algorithms can be evaluated visually via the input/output images and objectively via the input/output signal-to-noise ratio (SNR).     

Frisch scheme identification for dynamic diagonal bilinear models

The article addresses the problem of dynamic system identification in the errors-in-variables framework for a class of discrete-time time-invariant input–output bilinear models when subjected to a white input signal. The proposed algorithm is based on an extension of the bias-compensated least squares method and utilises the Frisch scheme equations to determine the parameter vector together with the variances of the input and output noise sequences. The appropriateness of the approach is analysed and its performance evaluated when compared to other errors-in-variables identification techniques by means of a Monte Carlo simulation. The results obtained demonstrate the accuracy of the proposed method and the performance in terms of noise robustness is also observed.     

Optimal nonparametric identification from arbitrary corrupt finitetime series

Formulates and solves a worst-case system identification problem for single-input, single-output, linear, shift-invariant, distributed parameter plants. The available a priori information in this problem consists of time-dependent upper and lower bounds on the plant impulse response and the additive output noise. The available a posteriori information consists of a corrupt finite output time series obtained in response to a known, nonzero, but otherwise arbitrary, input signal. The authors present a novel identification method for this problem. This method maps the available a priori and a posteriori information into an “uncertain model” of the plant, which comprises a nominal plant model, a bounded additive output noise, and a bounded additive model uncertainty. The upper bound on the model uncertainty is explicit and expressed in terms of both the l₁ and H_∞ system norms. The identification method and the nominal model possess certain well-defined optimality properties and are computationally simple, requiring only the solution of a single linear programming problem     

The minimization of measurement error in a general perturbation-correlation process identification system

A general identification system is studied for an important class of realistic, time-varying processes. This class consists of those in which the process is nominally known, and the statistical characteristics of its varying parameters and of the environment are also known. The expression for identification error in terms of the spectral properties of the parameter variations and of the output transducer noise is developed. Optimization procedures are given to minimize the perturbation-correlation system's mean-square identification error.     

闭环系统的输出过采样辨识方法及其估计精度分析

传统闭环系统辨识方法的可辨识性受到参考设定信号和控制器结构的限制．提出了一种通过对输出过采样实现线性离散时间闭环系统辨识的方法，输出过采样提供了更多的系统结构信息，在传统辨识方法的可辨识条件不满足的情况下，仍能正确辨识系统参数，针对有色噪声干扰，分析其在不同过采样率下的估计精度，得出最优估计的过采样率计算方法．辨识方法实现简单、运算量小、估计精度高．仿真试验验证了其有效性．     

基于异质多传感器的网络分布数据融合的一种算法

针对多异质传感器数据融合能够实现信息互补,改善目标跟踪精度,提出了一种异质多传感器异步量测融合算法,即首先将量测方程线性化,再在砷合中心通过建立伪量测方程,得到同步的量测数据,然后利用噪声相关的伪序贯思想进行融合处理得到全局估计,与现有算法进行仿真比较,结果表明了该算法的有效性。     

Sub-optimal bang-bang control of stochastic systems†

Much attention has been paid to the statistical linearization approach to the optimizing problem for stochastic systems. In this paper, a technique is presented for designing a sub-optimal bang-bang control law with a class of non-linear switching functions. The structural form of the non-linear switching function is prespecifled, while leaving free parameters to be chosen in a optimal fashion. Using statistical linearization, the free parameters are chosen so as to be independent of the external noise levels as well as to minimize the average cost. Detailed discussions are given of two typical examples.     

双线性状态空间系统的状态观测器设计

针对受过程噪声和量测噪声干扰的双线性状态空间系统,研究其状态估计算法.借助双线性系统的特殊结构,将其等价表示为线性时变模型,推导基于Kalman滤波的状态估计算法.针对线性时变模型中存在的未知变量,基于辅助模型辨识思想,通过构造一个辅助模型,将未知变量用该模型的输出代替,提出基于辅助模型的双线性系统状态估计算法.构造双线性状态观测器,引入delta算子极小化状态估计误差协方差矩阵,从而得到最优状态估计增益,并提出基于delta算子的双线性系统状态估计算法.所提出的算法能够避免线性化过程带来的估计精度差的问题,提高双线性系统的状态估计精度.通过仿真实验验证了所提出算法的有效性,并对比分析了不同噪声情况下所提出算法的估计效果.     

Closed-loop data-driven simulation

Closed-loop data-driven simulation refers to the problem of finding the set of all responses of a closed-loop system to a given reference signal directly from an input/output trajectory of the plant and a representation of the controller. Conditions under which the problem has a solution are given and an algorithm for computing the solution is presented. The problem formulation and its solution are in the spirit of the deterministic subspace identification algorithms, i.e. in the theoretical analysis of the method, the data is assumed exact (noise free). The results have applications in data-driven control, e.g. testing controller's performance directly from closed-loop data of the plant in feedback with possibly different controller.     

一类不确定非线性系统的指数鲁棒输出跟踪

研究一类不确定非线性系统的鲁棒输出跟踪控制问题。应用输入／输出反馈线性化法和李亚普诺夫方法,提出一种基于不确定项上界的连续型鲁棒输出跟踪控制器设计方法。该控制器不仅可确保闭环系统的状态一致最终有界,使系统输出按指数规律跟踪期望输出,而且计算简单,更易实现。仿真结果证明了该方法的可行性与有效性。     

具有区间时变时滞的离散Markov跳变系统鲁棒H∞控制

研究一类具有区间时变时滞的离散时间不确定Ｍａｒｋｏｖ跳变系统的时滞相关鲁棒H_∞ 控制问题．通过构造新的ＬｙａｐｕｎｏｖＫｒａｓｏｖｓｋｉｉ泛函,基于有限和不等式方法设计状态反馈控制器,使得闭环系统在容许不确定性下鲁棒稳定,且对能量有界的输入噪声满足一定输入输出H_∞ 增益．在新控制器存在条件中未引入任何自由变量矩阵,使之可更为有效地求解．基于锥补线性化的迭代算法可有效求解H_∞ 次优控制器．数值算例表明了所提出方法的有效性．     

Parameter identification of distributed parameter systems in the presence of measurement noise

A new approach to recursive parameter identification of second-order distributed parameter systems in the presence of measurement noise under unknown initial and boundary conditions is proposed. A two-dimensional low-pass filter is introduced to pre-filter the observed data corrupted by measurement noise. The low-pass filter is designed in the continuous time-space domain and discretized by bilinear transformation. Thus a discrete estimation model of the system under study is easily constructed with filtered input-output data for recursive identification algorithms. The recursive least squares method is still efficient in the presence of low measurement noise if the filter parameters are designed so that the noise effects are reduced sufficiently. Using filtered input data as instrumental variables, a recursive instrumental variable method is also presented to obtain consistent estimates when the digital low-pass filters are not designed successfully or when the output data is corrupted by high measurement noise. Illustrative examples are given to demonstrate the applicability of the proposed methods.     

Worst-case/deterministic identification in H∞: the continuous-time case

Results obtained by the authors (1991) worst-case/deterministic H_∞ identification of discrete-time plants are extended to continuous-time plants. The problem involves identification of the transfer function of a stable strictly proper continuous-time plant from a finite number of noisy point samples of the plant frequency response. The assumed information consists of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, an upper bound on the roll-off rate of the plant, and an upper bound on the noise level. Concrete plans of identification algorithms are provided for this problem. Explicit worst-case/deterministic error bounds for each algorithm establish that they are robustly convergent and (essentially) asymptotically optimal. Additionally, these bounds provide an a priori computable H_∞ uncertainty specification, corresponding to the resulting identified plant transfer function, as an explicit function of the plant and noise prior information and the data cardinality     

永磁直线电机的无模型自适应控制方法研究

将基于全格式线性化的单入单出非线性离散时间系统的无模型学习自适应控制方法应用在永磁直线电机的速度和位置控制中.控制器的设计是无模型的,是直接基于称为拟梯度的向量,拟梯度向量是通过新型参数估计算法,根据给出的永磁直流直线电机运动模型的输入输出信息在线导出的.无模型控制方法非常适用于实际的阶数难以知道或难以辨识,且是时变的非线性系统.实现了系统阶数较高时的有效控制,弥补了经典自适应控制阶数高时在线计算量过大而不能适应于系统快速变化过程的不足.利用Matlab软件进行仿真实验,验证了该方法对电机这种具有不确知动态的非线性系统的稳定性和抑止外部干扰和噪声的有效性和鲁棒性.