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Zbl 0933.37055
Mendes, Eduardo M.A.M.; Billings, S.A.
On overparametrization of nonlinear discrete systems. (English)
[J] Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No.3, 535-556 (1998). ISSN 0218-1274

Summary: One of the subjects which has received a great deal of attention is the overparametrization problem. It is known that the dynamical performance of the model representations deteriorates if the respective model structure is too complex. This paper investigates the problem of model overparametrization. Two new types of overparametrization, fixed-point and dimension overparametrization, are introduced and based upon this a new procedure for improving structure detection of nonlinear models is developed. This procedure uses all the information from the cluster cancellation and the location of the fixed points. Numerous examples are given to illustrate the ideas.

MSC 2000:: *37G35 Attractors and their bifurcations
37H15 Multiplicative ergodic theory, Lyapunov exponents
37C70 Attractors and repellers, topological structure
37L30 Attractors and their dimensions
37N35 Dynamical systems in control
93C35 Multivariable, multidimensional control systems
93E12 System identification (stochastic systems)

Keywords: nonlinear discrete systems; overparametrization problem; fixed-point; dimension

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