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

TL;DR

This paper introduces a novel method for optimizing the global stability of parameter-dependent dynamical systems by approximating them with finite-state Markov jump processes, avoiding trajectory simulations.

Contribution

It presents a new approach that simplifies stability optimization by linking parameters directly to objective functions through linear equations, without requiring trajectory simulations.

Findings

Efficient approximation of stability properties without trajectory simulation

Explicit relationship between parameters and objective functions

Applicable to a wide class of parameter-dependent systems

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.