Closed-loop persistent identification of linear systems with unmodeled dynamics and stochastic disturbances

The essential issues of time complexity and probing signal selection are studied for persistent identification of linear time-invariant systems in a closed-loop setting. By establishing both upper and lower bounds on identification accuracy as functions of the length of observation, size of unmodeled dynamics, and stochastic disturbances, we demonstrate the inherent impact of unmodeled dynamics on identification accuracy, reduction of time complexity by stochastic averaging on disturbances, and probing capability of full rank periodic signals for closed-loop persistent identification. These findings indicate that the mixed formulation, in which deterministic uncertainty of system dynamics is blended with random disturbances, is beneficial to reduction of identification complexity.     

On the assessment of multivariable controllers using closed loop data. Part I: Identification of system models

Controller performance assessment of SISO and MIMO systems requires effective and systematic identification of the associated system models based on closed-loop data. In this work, a new methodology for the identification of the process, controller and disturbance models is presented for the purpose of enabling the evaluation of the performance of MIMO control systems. The methodology is based on subspace identification algorithms for the identification of the controller, process and disturbance models from closed-loop data. However, identification of the process model is enhanced by the estimation of the associated interactor matrix via the Variable Regression Estimation technique, the existence of which is mathematically proved. The proposed identification methodology is applied to two 2 × 2 systems utilizing both step-response and PRBS closed-loop data.     

Projection-based identification algorithm for grey-box continuous-time models

In this paper, a new identification method for continuous-time models, which can handle various grey-box structures and has strong robustness, is presented. The proposed method is based on an incremental model update scheme and the projection onto the subspace which reflects the model structure. By utilising these schemes, robustness of other continuous-time system identification methods and versatility of generic optimisation algorithms can be integrated into the proposed method. The effectiveness of the proposed method is demonstrated through numerical examples related to a grey-box model in closed-loop system and systems with unknown time-delay.     

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 new recursive identification algorithm for singularity free adaptive control

Reportedly, guaranteeing the controllability of the estimated system is a crucial problem in adaptive control. In this paper, we introduce a least-squares-based identification algorithm for stochastic SISO systems, which secures the uniform controllability of the estimated system and presents closed-loop identification properties similar to those of the least-squares algorithm. The proposed algorithm is recursive and, therefore, easily implementable. Its use, however, is confined to cases in which the parameter uncertainly is highly structured.     

Closed-loop identification of systems with uncertain time delays using ARX-OBF structure

Closed-loop identification of systems with known time delays can be effectively carried out with simple model structures like Autoregressive with Exogenous Input (ARX) and Autoregressive Moving Average with Exogenous Input (ARMAX). However, when the system contains large uncertain time delay, such structures may lead to inaccurate models with significant bias if the time delay estimate used in the identification is less accurate. On the other hand, conventional orthonormal basis filter (OBF) model structures are very effective in capturing the dynamics of systems with uncertain time delays. However, they are not effective for closed-loop identification. In this paper, an ARX-OBF model structure which is obtained by modifying the ARX structure is shown to be effective in handling closed-loop identification of systems with uncertain time delays. In addition, the paper shows that this advantage of ARX-OBF models over simple ARX model is considerable in multi-step ahead predictions.     

连续时间模型的闭环子空间辨识

本文对直接使用采样数据进行连续系统的闭环子空间辨识问题进行了研究．将线性滤波方法与基于主 元分析的子空间辨识相结合,利用参考输入或者外部激励信号的高阶滤波变换的正交投影变量作为辅助变量,提出 了一种新的连续时间系统闭环子空间辨识算法．数值仿真表明了与其他算法相比,本文提出的算法具有很好的辨识 效果．     

Subspace identification using instrumental variable techniques

Subspace-based algorithms for system identification have lately been suggested as alternatives to more traditional techniques. Variants of the MOESP type of subspace algorithms are in addition to open-loop identification applicable to closed-loop and errors-in-variables identification. In this paper, a new instrumental variable approach to subspace identification is presented. It is shown how existing MOESP-algorithms can be derived within the proposed framework, simply by changing instruments and weighting matrices. A noteworthy outcome of the analysis is that an improvement of an existing MOESP method for errors-in-variables identification can be proposed.     

Input–output identification of controlled discrete manufacturing systems

The automated construction of discrete event models from observations of external system's behaviour is addressed. This problem, often referred to as system identification, allows obtaining models of ill-known (or even unknown) systems. In this article, an identification method for discrete event systems (DESs) controlled by a programmable logic controller is presented. The method allows processing a large quantity of observed long sequences of input/output signals generated by the controller and yields an interpreted Petri net model describing the closed-loop behaviour of the automated DESs. The proposed technique allows the identification of actual complex systems because it is sufficiently efficient and well adapted to cope with both the technological characteristics of industrial controllers and data collection requirements. Based on polynomial-time algorithms, the method is implemented as an efficient software tool which constructs and draws the model automatically; an overview of this tool is given through a case study dealing with an automated manufacturing system.     

Closed-loop subspace identification using the parity space

It is known that many subspace algorithms give biased estimates for closed-loop data due to the existence of feedback. In this paper we present a new subspace identification method using the parity space employed in fault detection in the past. The basic algorithm, known as subspace identification method via principal component analysis (SIMPCA), gives consistent estimation of the deterministic part and stochastic part of the system under closed loop. Column weighting for SIMPCA is introduced which shows improved efficiency/accuracy. A simulation example is given to illustrate the performance of the proposed algorithm in closed-loop identification and the effect of column weighting.     

Comments on "Parameter identification and control of linear discrete-time systems"

A new proof of convergence of the stochastic approximation algorithm for parameter identification of closed-loop linear discrete-time control systems is proposed. This algorithm relates very effectively in terms of a sufficient condition the stability properties of the closed-loop system with the convergence of the identification algorithms, which were previously treated independently.     

基于正交分解的递推子空间闭环辨识方法

为实现闭环系统在线辨识,提出递推正交分解闭环子空间辨识方法(RORT)。首先,根据闭环系统状态空间模型和数据间投影关系,构建确定-随机模型,并利用GIVENS变换实现投影向量的递推QR分解;然后,引入带遗忘因子的辨识算法,构建广义能观测矩阵的递推更新形式,以减少子空间辨识算法中QR分解和SVD分解的计算量;最后,针对某型号陀螺仪闭环系统进行实验。实验结果表明, RORT法的辨识拟合度高于91%,能够对陀螺仪闭环系统模型参数进行在线监测。     

The role of vector autoregressive modeling in predictor-based subspace identification

Subspace identification for closed loop systems has been recently studied by several authors. A class of new and consistent closed-loop subspace algorithms is based on identification of a predictor model, in a way similar as prediction error methods (PEM) do. Experimental evidence suggests that these methods have a behavior which is very close to PEM in certain examples. The asymptotical statistical properties of one of these methods have been studied recently allowing to show (i) its relation with CCA and (ii) that Cramér-Rao lower bound is not reached in general. Very little, however, is known concerning their relative performance.In this paper we shall discuss the link between these “predictor-based” methods; to this purpose we exploit the role which Vector Auto Regressive with eXogenous input models play in all these algorithms. The results of this paper provide a unifying framework under which all these algorithms can be viewed; also the link with VARX modeling have important implications as to computational complexity is concerned, leading to very computationally attractive implementations.We also hope that this framework, and in particular the relation with VARX modeling followed by model reduction will turn out to be useful in future developments of subspace identification, such as the quest for efficient procedures and the statistical analysis with finite-data.     

实现闭环系统参数─致估计的直接辨识方法

为了实现闭环系统参数的一致估计，提出了一种一致辨识闭环系统模型参数的偏差补偿最小二乘法。这种方法不需要事先假设系统模型阶次和通道时延满足一定的不等式，允许前向通道和反馈通道之一中的噪声为有色噪声，并且在其辨识过程中不需要对有色噪声建模。     

A novel approach to output feedback control of fuzzy stochastic systems

This paper investigates the problem of Hankel-norm output feedback controller design for a class of T–S fuzzy stochastic systems. The full-order output feedback controller design technique with the Hankel-norm performance is proposed by the fuzzy-basis-dependent Lyapunov function approach and the conversion on the Hankel-norm controller parameters. Sufficient conditions are established to design the controllers such that the resulting closed-loop system is stochastically stable and satisfies a prescribed performance. The desired output feedback controller can be obtained by solving a convex optimization problem, which can be efficiently solved by standard numerical algorithms. Finally, a Henon map system is used to illustrate the effectiveness of the proposed techniques.     

基于辅助变量的闭环系统子空间辨识

提出一种基于辅助变量的子空间辨识方法,适用于控制器信息未知以及参考输入已知的闭环系统参数辨识.通过将输入-输出数据块正交投影到辅助变量的行空间,直接得到扩展观测矩阵垂空间的估计.由此可从闭环系统中提取出对象模型信息,同时由SVD分解得到扩展观测矩阵与下三角Toeplitz矩阵的估计.给出了系统参数矩阵、噪声矩阵的计算方法.将所提出的子空间辨识方法应用于闭环动态的系统参数估计,其结果表明了该方法的有效性.     

Worst-case analysis of identification-BIBO robustness forclosed-loop data

This paper deals with the worst-case analysis of identification of linear shift-invariant (possibly) infinite-dimensional systems. A necessary and sufficient input richness condition for the existence of robustly convergent identification algorithms in l¹ is given. A closed-loop identification setting is studied to cover both stable and unstable (but BIBO stabilizable) systems. Identification (or modeling) error is then measured by distance functions which lead to the weakest convergence notions for systems such that closed-loop stability, in the sense of BIBO stability, is a robust property. Worst-case modeling error bounds in several distance functions are included     

Blind channel identification via stochastic approximation: constant step-size algorithms

This work is devoted to the study of a class of recursive algorithms for blind channel identification. Using weak convergence methods, the convergence of the algorithm is obtained and the rate of convergence is ascertained. The technique discussed can also be used in the analysis of rates of convergence for decreasing step-size algorithms.     

Identification of closed-loop systems with low-order controllers

A bias correction method without noise modelling was recently proposed for indirect identification of closed-loop systems. A key assumption used in deriving this method required that the order of the controller is not less than that of the open-loop plant. A significant feature of the results presented in this paper is the removal of this assumption to enable the method to be applicable to unbiased identification of closed-loop systems with low order controllers.     

Closed-loop subspace-based identification algorithm using third-order cumulants

The problem of closed-loop system identification for coloured noise system without any knowledge of feedback controller is considered. We develop a solution to this problem in the framework of subspace identification based on high-order cumulants. The key of the developed algorithm is using the properties that the third-order cumulants are insensitive to any coloured Gaussian noises. By post-multiplying a suitable instrumental variable to the noise terms, the cross third-order cumulants are constructed that become zero when the noises are Gaussian distributed, and meanwhile the column rank of extended observability matrix is maintained. Thus, the standard subspace identification algorithms can be extended to closed-loop system corrupted by arbitrary coloured noises. A numerical simulation is presented to demonstrate the proposed algorithm.