An Algorithm for System Identification of a Discrete-Time Polynomial System without Inputs

A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed time series. A major step of the algorithm is to construct a set of generators for the polynomial function from the past outputs to the future outputs. For this singular value decompositions and polynomial factorizations are used. An example is provided.