Parameter identifiability of nonlinear systems: The role of initial conditions. (English) Zbl 1034.93014
Identifiability is an important perequisite for model identification. It concerns uniqueness of the model parameters determined from the input-output data. In the late 1980s concepts of differential algebra has been introduced in control and system theory. Recently, differential algebra tools have been applied to the identifiability of dynamic systems described by polynomial equations. These methods exploit the characteristic set of the differential ideal generated by the polynomials defining the system. The authors prove that the identifiability test procedures based on differential algebra may fail for systems which are started at specific initial conditions. This problem is strictly related to the accessibility of the system from the given initial conditions. When the system is nonaccessible a new ideal that includes all differential polynomials vanishing at the solution of the dynamical system started from the initial conditions has to be calculated. An identifiability test is proposed which is convenient for systems with specific initial conditions.
Reviewer: Yves Cherruault (Paris)
Keywords:
initial conditions; a priori global identifiability; differential algebra; model identification; nonlinear system; accessibilityReferences:
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