Model Reduction for Systems with Low-Dimensional Chaos
A method for deriving a reduced model of a continuous-time dynamical system with low-dimensional chaos is discussed. The method relies on the identification of peak-to-peak dynamics, i.e. the possibility of approximately (but accurately) predicting the next peak amplitude of an output variable from the knowledge of at most the two previous peaks. The reduced model is a simple one-dimensional map or, in the most complex case, a set of one-dimensional maps. Its use in control system design is discussed by means of some examples.
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