Optimizing the stable behavior of parameter-dependent dynamical systems --- maximal domains of attraction, minimal absorption times

Péter Koltai; Alexander Volf

doi:10.3934/jcd.2014.1.339

Article Contents

2014, Volume 1, Issue 2: 339-356. Doi: 10.3934/jcd.2014.1.339

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Optimizing the stable behavior of parameter-dependent dynamical systems --- maximal domains of attraction, minimal absorption times

Péter Koltai^1, and
Alexander Volf^2,

1.
Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin
2.
Klinikum rechts der Isar der Technischen Universität München, Dept. of Plastic and Reconstructive Surgery, Ismaninger Straße 22, München

Received: September 30, 2011

Revised: April 30, 2012

Published: May 2014

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Abstract

We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the infinite-state deterministic system by a finite-state non-deterministic one --- a Markov jump process. The key properties of the method are that it does not use any trajectory simulation, and that the parameters and objective function are in a simple (and except for a system of linear equations) explicit relationship.

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Mathematics Subject Classification: Primary: 34D23, 31C20; Secondary: 37C75, 60J27, 37M99.

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