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Abstract
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| In this chapter, to be dedicated in the 90th birthday of Professor C. S. Hsu, several computational schemes are presented for the optimal tuning of the global behavior of nonlinear dynamical systems. Specifically, the maximization of the size of domains of attraction associated with invariants in parametrized dynamical systems is addressed. Cell Mapping (CM) techniques are used to estimate the size of the domains for different parameter values, and such size function is then maximized via several optimization methods. First, a genetic algorithm is tested whose performance shows to be good for determining global maxima at the expense of high computational cost. Secondly, an iterative scheme based on a Stochastic Approximation procedure (the Kiefer-Wolfowitz algorithm) is evaluated showing acceptable performance at low cost. Finally, several schemes combining neural network based estimations and model-based optimization procedures are addressed with promising results. The performance of the methods is illustrated with some applications including the well-known van der Pol equation with standard parametrization, and the tuning of a controller for saturated systems. | |
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International
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Si |
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10.1007/978-1-4614-3128-2 |
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Book Edition
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1 |
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Book Publishing
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Springer Science + Businee Media, LLC, New York, USA |
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ISBN
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978-1-4614-3127-5 |
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Series
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Book title
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Global Analysis of Nonlinear Dynamics |
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From page
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31 |
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To page
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50 |