A new approach of the partial control method in chaotic systems
Abstract
We present here a new approach of the partial control method, which is a useful control technique applied to transient chaotic dynamics affected by a bounded noise. Usually we want to avoid the escape of these chaotic transients outside a certain region of the phase space. For that purpose, there exists a control bound such that for controls smaller than this bound trajectories are kept in a special subset of called the safe set. The aim of this new approach is to go further, and to compute for every point of the minimal control bound that would keep it in . This defines a special function that we call the safety function, which can provide the necessary information to compute the safe set once we choose a particular value of the control bound. This offers a generalized method where previous known cases are included, and its use encompasses more diverse scenarios.
Cite
@article{arxiv.1902.06238,
title = {A new approach of the partial control method in chaotic systems},
author = {Rubén Capeáns and Juan Sabuco and Miguel A. F. Sanjuán},
journal= {arXiv preprint arXiv:1902.06238},
year = {2019}
}