Model Identification and Data Analysis

4Model Identification

4.1 Introduction

Capturing in mathematical form phenomena of the real world has been a main objective of human beings since time immemorial. An example is the description of the motion of planets of the solar system, which captured the attention of many scholars over several centuries. With the growth of the industrial world, systems modeling has become essential for proper design in all fields. In this chapter, we present the main methods enabling the construction of mathematical models from data.

Often models are obtained by describing every constitutive element with an appropriate mathematical law, found in the history of this or that discipline. For instance, in the mathematical model of a ship, there will be variables corresponding to the driving force of the propeller, to the position of the rudder, to the external disturbances (wind and waves), and to the movement of the ship. The relationships that link these variables will be arrived at by drawing on the wealth of laws of mechanics and hydraulics. Though rather basic, this approach to constructing models can come up against a series of difficulties. The link between certain variables can be uncertain, either in its analytic characterization or due to the unknown value of a relevant parameter; in other words, one does not always have at hand a law to describe a given phenomenon with the necessary accuracy. Another difficulty is related to the notable complexity of some systems. The mathematical model ...