Abstract
We describe a local identification procedure for a class of nonlinear systems having bifurcations of known codimension. To perform such an algorithm, it is required that the tangent linear model at the bifurcation and the codimension of this bifurcation are known. We also assume that the measurements of the inputs and outputs are not corrupted by random noise. A vector field and an output function depending on the time derivatives of the inputs can thus be obtained by means of the normal form associated to the “cascade” of bifurcations produced by successively using inputs which are constant, affine with respect to time, quadratic and so on. Numerical methods are sketched.
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Cohen de Lara, M., Lévine, J. (1991). Local Identification of Nonlinear Systems, Bifurcations and Normal Forms. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_28
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DOI: https://doi.org/10.1007/978-1-4612-3214-8_28
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