In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function $\varphi $. We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or less complete...

In this paper, we consider general nonlinear systems with observations,
containing a (single) unknown function . We study the possibility to
learn about this unknown function the observations: if it is possible to
determine the [values of the] unknown function from any experiment [on the set
of states visited during the experiment], and for any arbitrary input
function, on any time interval, we say that the system is “identifiable”.
For systems without controls, we give a more or less complete...

We introduce a simple and powerful procedure-the observer method-in order to obtain a reliable method of numerical integration over an arbitrary long interval of time for systems of ordinary differential equations having first integrals. This aim is achieved by a modification of the original system such that the level manifold of the first integrals becomes a local attractor. We provide a theoretical justification of this procedure. We report many tests and examples dealing with a large spectrum...

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