Time Variant Nonlinear System Identification by Distributions; Application for Wastewater Biodegradation Process

This paper presents a procedure for time variant nonlinear system identification based on distribution theory. Some of the system parameters change in time according to unknown laws. These laws are expressed as finite degree time polynomials whose parameters are included in the set of parameters to be identified. Mainly it is an extension of the procedure developed in (Marin et al., 2005). Considering functionals weighted by polynomials, it is possible to transform a time variant differential system of equations to an algebraic system in unknown parameters. The hierarchical structure identification method for rational expressions, proposed in (Marin et al., 2005), is now extended to time variant systems. An application for parameter identification of a wastewater biodegradation process, considering time variant yield coefficients is presented.