Open AccessDetecting and stabilizing periodic orbits of chaotic Henon map through predictive control
Author(s) -
Dumitru Deleanu
Publication year - 2018
Publication title -
annals
Language(s) - English
Resource type - Journals
ISSN - 2067-0427
DOI - 10.38130/cmu.2067.100/42/12
Subject(s) - model predictive control , attractor , hénon map , periodic orbits , mathematics , chaotic , control theory (sociology) , term (time) , integer (computer science) , nonlinear system , state (computer science) , control (management) , computer science , algorithm , mathematical analysis , artificial intelligence , physics , quantum mechanics , programming language
The predictive control method is one of the proposed techniques based on the location and stabilization of the unstable periodic orbits (UPOs) embedded in the strange attractor of a nonlinear mapping. It assumes the addition of a small control term to the uncontrolled state of the discrete system. This term depends on the predictive state ps + 1 and p(s + 1) + 1 iterations forward, where s is the length of the UPO, and p is a large enough nonnegative integer. In this paper, extensive numerical simulations on the Henon map are carried out to confirm the ability of the predictive control to detect and stabilize all the UPOs up to a maximum length of the period. The role played by each involved parameter is investigated and additional results to those reported in the literature are presented.