系统辨识：理论与外文原著综述

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"系统辨识--外文原著"这一主题深入探讨了在工程设计与决策中遇到的关键挑战——不确定性，特别是对于控制系统的设计，我们往往对被控过程的特性以及可能影响其运行的干扰因素了解不足。系统辨识与建模作为一种处理这种不确定性问题的重要方法，旨在通过利用现有信息构建数学模型，同时通过实验获取更多有益的数据。首先，作者Lennart Ljung，作为瑞典林雪平大学电气工程系的专家，从系统的整体视角出发，为读者提供了一个系统辨识和建模的基本介绍。他的工作重点在于概述该领域的核心概念和一般性原则，而非局限于特定的算法讨论。在第二部分（第2节），他详细阐述了模型的概念，强调模型是理解系统行为的基础工具，它帮助我们捕捉系统的动态特性和输入输出关系。模型可以是理论的、基于经验的，或者结合两者，以便更准确地描述实际系统。紧接着，在第三部分（第3节），作者聚焦于系统识别问题，这是整个流程的核心环节。这里涉及如何从数据中提取有用的信息，包括系统的阶次、参数和结构，以及如何通过频域分析或时域分析来估计这些参数。时域分析，如自相关函数和功率谱分析，提供了关于信号随时间变化的直接信息，这对于确定系统的动力学特征至关重要。第四部分（第4节）进一步深入探讨了时间域分析模型，这部分内容可能会涵盖模型类型的选择（如ARIMA模型、灰色系统理论等）、模型参数的估计方法（如最小二乘法、卡尔曼滤波等）、以及模型验证和误差分析，以确保模型的准确性和可靠性。最后，整个过程可能还包括模型的不断优化和迭代，因为即使初始的模型可能不完美，通过持续的实验和数据收集，我们可以逐步提升模型的精度，从而更好地理解和控制实际系统。总结来说，系统辨识--外文原著这一主题涵盖了从理论基础到实际应用的广泛内容，旨在帮助工程师们面对并解决不确定性带来的设计挑战。"

= 1

UN(~) ~r~ ~ u(t)e -i~t

t=l

where YN and U N are the discrete Fourier transforms (DFT) of the out-

put and input sequences using N data. When noise affects the systems

(8) is usually a bad estimate ("the periodogram estimate"), since no

noise reduction is obtained. Instead various smoothing filters are

applied to (8): weighted averages over certain frequency windows are

formed. Such techniques are known as spectral analysis and are

further described in e.g. Jenkins and Watts (1968) and Brillinger

(1981) The estimate can thus be written

GN(ei~ ) = f W..(~-W)GN(ei~)d~

(9)

where W (C) is a weighting function that typically has its "mass"

concentrated arouind ~=0. See also Ljung (1984).

Analytical models. Most modern identification methods deal with the

estimation of analytical models, usually described in the time domain.

More detailed descriptions of such methods will be given in Section 5.

See also Goodwin and Payne (1977), Astr~m (1980) and Astr~m and Eyk-

hoff (1971). The basic idea behind such methods is the following one:

Let each of the candidate models "guess" (predict) the next output

y(t) based on the information in Z t-1. Pick that model that produces

the best ("smalles~') sequence of errors between guesses and actually

recorded outputs. These identification methods are thus characterized

by a criterion of fit between a model and the recorded sequence of

data.

The Identification Procedure

The identification procedure is, from a principal point of view, desc-

ribed by the three items listed above: Data, Model set, and Identifi-

cation criterion. From a practical point of view the procedure is

characterized by a number of choices which we now list.

Experiment Design. How to design the identification experiment, so

that it becomes suitably informative. Choice of inputs, sampling ra-

tes, presampling filters, feedback configurations, choice of signals

to be measured, etc. Such aspects are further discussed in Goodwin and

Pavne (1977).

Choice of Model Set. To select the set of candidate models. This is no

doubt the most important and, at the same time, the most difficult

choice. It is here that a priori knowledge and engineering intuition

and insight has to be combined with formal properties of models and

identification methods to facilitate a good result from the identifi-

cation exercise.

Choice of criterion of fit. How to evaluate the quality of a particu-

lar model from data is a crucial issue, which is further discussed in

Section 5.

Calculation of the best model. With given data and a fixed model set

and a chosen criterion of fit, the "best" model is implicitly defined.

It remains "only" to calculate it, which may involve extensive compu-

tations. Good numerical algorithms are required in order to allow for

reliable and inexpensive calculations. Some computational aspects are

included in Ljung (1982). See also Gupta and Mehra (1974), and Dennis

and Schnabel (1983).

In several applications, the models are required on-line, as the sys-

tem operates and more data becomes available. The reason could be that

the models are to be used for some on-line decision like control

(adaptive control), filter tuning (e.g. adaptive noise cancellation)

or monitoring (fault detection). This implies certain restrictions for

how to calculate the estimates. Such methods are called recursive

identification methods (or on-line or real-time identification) and

are discussed, e.g., in Ljung and S~derstr~m (1983).

Model validation. Once the best model available in the model set has

been determined it remains to test whether it is "good enough", i.e.

whether it is valid for its purpose. This is the problem of model

validation, which is further described in Section 8.

The whole identification procedure is typically an iterative one, in

which earlier made choices have to be revised after the model valida-

tion step and portions of the procedure repeated. This is illustrated

in figure i.

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