Linear and optimal non-linear control of one-dimensional maps

Abstract

We investigate the effects of linear and optimal non-linear control in the simple case of one-dimensional unimodal maps. We show that linear feedback relates unimodal maps to invertible "Hénon-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 non-linear 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. Show more