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Journal of Control Science and Engineering
Volume 2018, Article ID 3298286, 21 pages
https://doi.org/10.1155/2018/3298286
Research Article

Approximate Prediction-Based Control Method for Nonlinear Oscillatory Systems with Applications to Chaotic Systems

1Universidade Estadual de Santa Cruz (UESC), 45662-900 Ilhéus, BA, Brazil
2Lab. J.-L. Lions UMR CNRS, Inria, UPMC University Paris 06, Sorbonne Universités, 7598 Paris, France
3Fundação Getúlio Vargas, Rio de Janeiro, RJ, Brazil
4Instituto Tecnológico de Aeronáutica (ITA), 12228-900 São José dos Campos, SP, Brazil

Correspondence should be addressed to Thiago P. Chagas; moc.liamg@sagahcht

Received 22 October 2017; Revised 15 December 2017; Accepted 19 December 2017; Published 1 March 2018

Academic Editor: Sundarapandian Vaidyanathan

Copyright © 2018 Thiago P. Chagas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The approximate Prediction-Based Control method (aPBC) is the continuous-time version of the well-known Prediction-Based Chaos Control method applied to stabilize periodic orbits of nonlinear dynamical systems. The method is based on estimating future states of the free system response of continuous-time systems using the solution from the Runge-Kutta implicit method in real time. Some aspects of aPBC are evaluated in the present work, particularly its robustness to low future states estimation precision is exemplified.