Tutorial on System Identification of Polynomial and of Rational Systems

The aim of this tutorial paper is to provide an overview of system identification of polynomial and of rational systems. It is an introduction to a session included in the program of the IFAC Symposium System Identification (SYSID.2009). Polynomial and rational systems arise in systems biology where there is a great need to have algorithms and methods for obtaining realistic models. The paper presents a system identification procedure for these classes of systems consisting of: (1) Modeling; (2) Experiment design and data processing; (3) Identifiability; (4) Approximation; and (5) Evaluation. Major open problems include the approximation problem and computer-algebra algorithms for checking identifiability.