Introduction to Modeling and Simulation

9System Identification

9.1 Introduction

In this chapter we give an introduction to system identification. Roughly speaking, system identification involves the use of measured data to determine the best model for a given system. We will primarily focus on regression and parameter estimation. In this case we assume that we have a model of our system expressed in terms of certain parameters and the task is to estimate the values of the parameters from input/output measurements.

Some key questions to consider are:

• How to generate “sufficiently rich input data.” In other words, how to choose inputs so that the system can be identified accurately.
• What are the assumptions on the model structure? It may be linear or nonlinear, parametric or nonparametric.
• How to validate the model? How good a fit is the model? Can it predict outputs for new inputs?

Before continuing to the next section, the reader should review the concepts of range and null space of a linear transformation in Appendix A.

9.2 Least Squares

The method of least squares has a rich and interesting history [53]. The best‐known anecdote is the story of the mathematician Karl Friedrich Gauss's prediction of the location of the asteroid Ceres. On New Year's Day in 1801, the Italian astronomer Giuseppe Piazzi discovered Ceres and was able to track its path for 40 days until it passed behind the Sun. The problem then posed by astronomers was how to predict the location of Ceres when it emerged from behind the Sun. Gauss's ...