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Nonlinear Dynamics: Weak, Strong, and Intermediate


R. Pearson

Lausanne, Switzerland, L'Institut d'automatique, EPFL

At the 1993 European Control Conference in Groningen, Frank Doyle, Tunde Ogunnaike and I presented a paper describing a ``process characterization cube'' with axes labelled as: (1) degree of nonlinearity, (2) dynamic character, and (3), degree of interaction. The motivation for this construction was to classify process units, multi-unit configurations, or process operating conditions in a way that would help in selecting compatible control strategies. This talk revisits some of these ideas, initially focusing on the nonlinearity axis but illustrating some of the interesting ways these three axes are interdependent. A particularly useful notion that emerges is the classification of nonlinear dynamic models into three subsets: weakly nonlinear, strongly nonlinear, and intermediate nonlinearity. Prototypes of these classes are the nonlinear FIR models, the polynomial NARMAX models, and the bilinear models, respectively: the first case is generically well-behaved, the second generally exhibits complicated dynamics (e.g., amplitude-dependent step responses that vary from monotonic to oscillatory to chaotic to unstable), and the third exhibits some but not all of these forms of nonlinear behavior. Both SISO and MIMO models are considered to illustrate the interplay between the three axes of the process characterization cube.


Type of Publication:

(05)Plenary/Invited/Honorary Lecture

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