Some remarks about identifiability of controlled and uncontrolled nonlinear systems

The problem of identifiability of parameters is solved more easily in the case of controlled systems than in the case of uncontrolled systems. Indeed when there exists an input-output operator, the similarity transformation approach [8] [5] gives a system of partial differential equations of which solution can he found by a systematic procedure [1]. On the other hand, when the nonlinear system is not controlled and if the linearization approach does not work, the power series expansion [7] is a possible approach to give some results of identifiability. Then the computations are very complicated even with the help of symbolic manipulation softwares and it gives local identifiability results [6] [9J. In this paper, it is shown, by means of some examples, that it is possible to get global identifiability results for uncontrolled-nonlinear systems in using not one experiment but various experiments.