  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.
