Low-Rank Tensor Decompositions for Nonlinear System Identification: A Tutorial with Examples

Nonlinear parametric system identification is the estimation of nonlinear models of dynamical systems from measured data. Nonlinear models are parameterized, and it is exactly these parameters that must be estimated. Extending familiar linear models to their nonlinear counterparts quickly leads to practical problems. For example, the generalization of a multivariate linear function to a multivariate polynomial implies that the number of parameters grows exponentially with the total degree of the polynomial. This exponential explosion of model parameters is an instance of the so-called curse of dimensionality. Both the storage and computational complexities are limiting factors in the development of system identification methods for such models.