The Dimension Estimation Problem for Nonlinear Systems

We consider the dimension estimation problem for nonlinear systems, that is, the problem of finding the least possible dimension of the state space of a (minimal) realization of a nonlinear system from given input-output measurements. Exploiting tools from nonlinear realization theory and free Lie algebras, we develop algorithms to solve the dimension estimation problem both for bilinear and for general nonlinear systems, provided sufficient measurements are available. Simple worked-out examples illustrate the theory.