Abstract
This paper addresses the problem of identifiability of nonlinear polynomial state-space systems. Such systems have already been studied via the input-output equations, a description that, in general, requires differential algebra. The authors use a different algebraic approach, which is based on distinguishability and observability. Employing techniques from algebraic geometry such as polynomial ideals and Gröbner bases, local as well as global results are derived. The methods are illustrated on some example systems.
Highlights
Dynamical systems are usually described by a set of differential or differentialalgebraic equations
The Lie derivative of a vector of scalar fields yields a vector of scalar fields again, where the Lie derivative is applied to each vectorial component [34]
The problem of deciding global or local identifiability of a system has been addressed by viewing the parameters as additional state variables and testing the observability of these
Summary
Dynamical systems are usually described by a set of differential or differentialalgebraic equations These mathematical models may originate from physical laws and the known structure of that system. Structural identifiability asks for the feasibility to compute the parameters from the inputoutput behaviour of the mathematical model without noise or uncertainties This is often not useful if the identification problem is ill-conditioned. This article considers a method that does not rely on a differential ring and can determine the identifiability using computations in the ordinary polynomial ring [27,28,29] alone The computation in this simpler domain comes at the cost of more variables that are required to formulate the problem.
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