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Research Report MRR97-024
Linear and optimal nonlinear control of one-dimensional maps
Justin McGuire, Murray T. Batchelor,
Brian Davies
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.
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