Identification of complex systems

In this paper, we discuss the problem of identifying a complex system with a limited-complexity model using finite corrupted data. Complex systems are ones that cannot be uniformly approximated by a finite dimensional space. Nevertheless, our prejudice is represented by selecting a finitely paramete rized set of models from which an estimate of the original system will ulti mately be drawn. We will give an account of a new formulation that shows ho w such a model should be selected from data. We will demonstrate this parad igm on the class of linear time-invariant stable systems and give an overvi ew of the available results concerning input design, consistency, error bou nds, and sample complexity.