Linear and optimal nonlinear control of one-dimensional maps

Details Linear and optimal nonlinear control of one-dimensional maps Linear and optimal nonlinear control of one-dimensional maps

1997-04-09

arxiv.org/abs/chao-dyn/9704013v1

Phys. Lett. A 233 (1997) 361-364

Nonlinear Sciences

Chaotic Dynamics

7 pages, Latex, no figures

Scientific paper

10.1016/S0375-9601(97)00486-6

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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