Parametric identification of structured nonlinear systems

In this paper, identification of structured nonlinear systems is considered. Using linear fractional transformations (LFT), the a priori information regarding the structural interconnection is systematically exploited. A parametric approach to the identification problem is investigated, where it is assumed that the linear part of the interconnection is given and the input to the nonlinear part is measurable. An algorithm for the identification of the nonlinear part is proposed. The uniqueness properties of the estimate provided by the algorithm are examined. It is shown that the estimate converges asymptotically to its true value under a certain persistence of excitation condition. Two simulated examples and a real-data example are presented to show the effectiveness of the proposed algorithm.     

Identification of nonlinear systems using a piecewise-linear Hammerstein model

In the paper a method for nonlinear system identification is proposed. It is based on a piecewise-linear Hammerstein model, which is linear in the parameters. The model and the identification algorithm are adapted to allow the parameter identification in the presence of a special form of the excitation signal. The identification method is derived from a recursive least-squares algorithm, which is properly adapted to take into account the proposed model structure and the properties of the identification signal. The applicability of the approach is illustrated by an example in which a discontinuous nonlinear static function is connected to a dynamic block.     

Subspace identification of MIMO LPV systems using a periodic scheduling sequence

A novel subspace identification method is presented which is able to reconstruct the deterministic part of a multivariable state-space LPV system with affine parameter dependence, in the presence of process and output noise. It is assumed that the identification data is generated with the scheduling variable varying periodically during the course of the identification experiment. This allows to use methods from LTI subspace identification to determine the column space of the time-varying observability matrices. It is shown that the crucial step in determining the original LPV system is to ensure the obtained observability matrices are defined with respect to the same state basis. Once the LPV model has been identified, it is valid for other nonperiodic scheduling sequences as well.     

Trends in identification

The paper refers to methods used for identification of linear and nonlinear systems. Deterministic and stochastic approaches are distinguished and specific features concerning parameters, structure and state estimation are briefly discussed from the point of view of possible advantages and difficulties for identification. Attention is paid to different final goals of identification with respect to the convenience of the methods in question. The most important trends in identification approaches are argued by unsolved problems of identification, by the complexity of numerical calculations and of practical applications. The significance of the uncertainty in structure, parameters or noise and the possible application of the a priori knowledge of the analysed system are taken into consideration.     

Making parametric Hammerstein system identification a linear problem

In this paper, we study the identification of parametric Hammerstein systems with FIR linear parts. By a proper normalization and a clever characterization, it is shown that the average squared error cost function for identification can be expressed in terms of the inner product between the true but unknown parameter vector and its estimate. Further, the cost function is concave in the inner product and linear in the inner product square. Therefore, the identification of parametric Hammerstein systems with FIR linear parts is a globally convergent problem and has one and only one (local and global) minimum. This implies that the identification of such systems is a linear problem in terms of the inner product square and any local search based identification algorithm converges globally.     

Fast approximate identification of nonlinear systems

In this paper, a method is presented to extend the classical identification methods for linear systems towards nonlinear modelling of linear systems that suffer from nonlinear distortions. A well chosen, general nonlinear model structure is proposed that is identified in a two-step procedure. First, a best linear approximation is identified using the classical linear identification methods. In the second step, the nonlinear extensions are identified with a linear least-squares method. The proposed model not only includes Wiener and Hammerstein systems, it is also suitable to model nonlinear feedback systems. The stability of the nonlinear model can be easily verified. The method is illustrated on experimental data.     

Simultaneous Constrained Model Predictive Control and Identification of DARX Processes

In this work, we formulate a new approach to simultaneous constrained model predictive control and identification (MPCI). The proposed approach relies on the development of a persistent excitation (PE) criterion for processes described by DARX models. That PE criterion is used as an additional constraint in the standard on-line optimization of MPC. The resulting on-line optimization problem of MPCI is handled by successively solving a series of semi-definite programming problems. Advantages of MPCI in comparison to other closed-loop identification methods are (a) Constraints on process inputs and outputs are handled explicitly, (b) Deterioration of output regulation is kept to a minimum, while closed-loop identification is performed. The applicability of the method is illustrated by a number of simulation studies. Theoretical and computational issues for further investigation are suggested.     

A blind approach to the Hammerstein-Wiener model identification

In this paper, we propose a blind approach to the sampled Hammerstein-Wiener model identification. By using the blind approach, it is shown that all internal variables can be recovered solely based on the output measurements. Then, identification of linear and nonlinear parts can be carried out. No a priori structural knowledge about the input nonlinearity is assumed and no white noise assumption is imposed on the input.     

Multi-output process identification

In model based control of multivariate processes, it has been common practice to identify a multi-input single-output (MISO) model for each output separately and then combine the individual models into a final MIMO model. If models for all outputs are independently parameterized then this approach is optimal. However, if there are common or correlated parameters among models for different output variables and/or correlated noise, then performing identification on all outputs simultaneously can lead to better and more robust models. In this paper, theoretical justifications for using multi-output identification for a multivariate process are presented and the potential benefits from using them are investigated via simulations on two process examples: a quality control example and an extractive distillation column. The identification of both the parsimonious transfer function models using multivariate prediction error methods, and of non-parsimonious finite impulse response (FIR) models using multivariate statistical regression methods such as partial least squares (PLS2), canonical correlation regression (CCR) and reduced rank regression (RRR) are considered. The multi-output identification results are compared to traditional single-output identification from several points of view: best predictions, closeness of the model to the true process, the precision of the identified models in frequency domain, stability robustness of the resulting model based control system, and multivariate control performance. The multi-output identification methods are shown to be superior to the single-output methods on the basis of almost all the criteria. Improvements in the prediction of individual outputs and in the closeness of the model to the true process are only marginal. The major benefits are in the stability and performance robustness of controllers based on the identified models. In this sense the multi-output identification methods are more ‘control relevant’.     

Efficient nonparametric identification for high-precision motion systems: A practical comparison based on a medical X-ray system

The need for accurate knowledge of complex dynamical behavior for high-performance mechatronic systems led to the development of a vast amount of nonparametric system identification approaches over the recent years. The aim of this paper is to compare several proposed methods based on experiments on a physical complex mechanical system to bridge the gap between identification theory and practical applications in industry where basic identification approaches are often the norm. Typical practical implications such as operation under closed-loop control, multivariable coupled behavior and nonlinear effects are included in the analysis. Finally, a possible approach for fast and reliable identification is illustrated based on measurement results of an interventional medical X-ray system.     

基于理性遗传算法的模糊系统辨识

针对模糊系统辨识的复杂问题,提出基于理性遗传算法的模糊系统辨识。模糊系统辨识包括前件结构、参数辨识和后件结构、参数辨识,在利用模糊系统的通用逼近性的基础上,采用理性遗传算法对模糊模型进行辨识,并给出仿真结果,其结果表明理性遗传算法在进行离线辨识中是一种十分有效的方法。     

Identification of linear systems with hard input nonlinearities of known structure

This paper studies identification of systems with input nonlinearities of known structure. For input nonlinearities parameterized by one parameter, a deterministic approach is proposed based on the idea of separable least squares. The identification problem is shown to be equivalent to an one-dimensional minimization problem. The method is very effective for several common static and nonstatic input nonlinearities. For a general input nonlinearity, a correlation analysis based identification algorithm is presented which is shown to be convergent.     

Active identification and control given bounded noise (disturbances)

Problems of active identification and control with bounded disturbances are considered for two classes of plants: dynamic plants and those without memory. Performance criteria of set-membership identification are proposed for each of the classes. For controlled plants without memory, an algorithm of optimal design of experiments is developed which provides a minimum of performance criterion of set-membership identification. Only a suboptimal solution of the problem is obtained for the class of dynamic systems. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 147–157, January–February, 2000. This work has been carried out with support from the State Fund for Fundamental Studies (Project 1.4/370) and Grant FWF (Austria) (Project 13706/MAT).     

Identification test design for multivariable model-based control: An industrial perspective

The design of plant tests to generate data for identification of dynamic models is critically important for development of model-based process control systems. Multivariable process identification tests in industry continue to rely on uncorrelated input signals, even though investigations have shown the benefits of other input designs which lead to correlated, higher-amplitude input signals. This is partly due to difficulties in formulating and solving computationally tractable problems for identification test design. In this work, related results are summarized and extended. Connections between different designs that target D-optimality or integral controllability are established. Related concepts are illustrated through simulation case studies.     

非线性系统辨识

本文综述了非线性系统辨识问题，包括描述非线性系统的模型结构的辨识，模型参数的估计，并对可能的发展方向提出了作者的观点，最后介绍非线性系统辨识的若干应用。     

一类非线性离散时间系统的模糊辨识

对一类非线性离散时间系统提出了模糊辨识方法,此方法用与未知参数向量成线性关系的模糊逻辑系统作为辨识模型,并通过自适应学习律对此模糊逻辑系统中的未知参数进行自适应调节,文中证明了此方法可使辨识误差收敛到原点的一个邻域内。仿真结果验证了此方法的有效性。     

Multivariable system identification for integral controllability

Integral controllability is necessary and sufficient for a multivariable model to be usable in a decoupling controller with integral action that can be arbitrarily detuned without jeopardizing closed-loop robust stability. The design of experiments for identification of integral controllable models is challenging, because it must satisfy cumbersome eigenvalue inequalities involving a coupling between the real system and its model. To address this challenge, an optimization-based mathematical framework is developed that characterizes efficient identification experiments ensuring integral controllability. The proposed framework recovers well known experiment designs but also produces new ones of both theoretical and practical interest. Such designs are expressed either analytically or as a result of numerical optimization and are demonstrated in a number of examples. These designs can be easily implemented in industrial practice. By combining additional objectives or constraints of interest, the proposed framework can further serve as a basis for new experiment designs in future work.     

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.