System identification
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System identification is a general term to describe mathematical tools and algorithms that build dynamical models from measured data. A dynamical model in this context is a mathematical description of the dynamic behavior of a system or process. Examples include:
- physical processes such as the movement of a falling body under the influence of gravity
- economical processes such as stock markets that react to external influences
One could build a so-called white-box model based on first principles, eg. a model for a physical process from the Newton equations, but in many cases such models will be overly complex and possibly even impossible to obtain in reasonable time due to the complex nature of many systems and processes.
A much more common approach is therefore to start from measurements of the behavior of the system and the external influences (inputs to the system) and try to determine a mathematical relation between them without going into the details of what is actually happening inside the system. This approach is called system identification. Two types of models are common in the field of system identification:
- grey box model: although the peculiarites of what is going on inside the system are not entirely known, a certain model is already available. This model does however still have a number of unknown free parameters which can be estimated using system identification.
- black box model: No prior model is available. Most system identification algorithms operate in this field.