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

2011/11/02 by Koltai, Péter, Volf, Alexander
#37M99 #65P99 #93C15 #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1111.0495

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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