English

Linear and optimal nonlinear control of one-dimensional maps

chao-dyn 2009-10-30 v1 Chaotic Dynamics

Abstract

We investigate the effects of linear and optimal nonlinear control in the simple case of one-dimensional unimodal maps. We show that linear feedback relates unimodal maps to invertible ``Henon-like'' maps. This observation should be useful in relating the considerable bodies of knowledge which exist for the two types of systems. In the case of the optimal nonlinear feedback scheme of de Sousa Vieira and Lichtenberg we investigate the relationship between controlled and uncontrolled maps, particularly the preservation of the period doubling route to chaos.

Cite

@article{arxiv.chao-dyn/9704013,
  title  = {Linear and optimal nonlinear control of one-dimensional maps},
  author = {Justin McGuire and Murray T. Batchelor and Brian Davies},
  journal= {arXiv preprint arXiv:chao-dyn/9704013},
  year   = {2009}
}

Comments

7 pages, Latex, no figures

R2 v1 2026-07-22T09:55:39.178Z