Operator-Orthoregressive Method for Identifying Coefficients of Linear Differential Equations

We propose an approach to identify coefficients of linear differential equations from observations of solutions with additive perturbations, based on the algebraic Fliess–Sira-Ramirez method combined with the orthogonal regression method in the space of observed functions that are transformed by convolution type integral operators. We establish the consistency of the operator-orthoregressive method and numerically analyze asymptotical properties and computational complexity of the proposed method in comparison with the asymptotically optimal variational method of identification.