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

Justin McGuire; Murray T. Batchelor; Brian Davies

doi:10.1016/S0375-9601(97)00486-6

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

Justin McGuire^*, Murray T. Batchelor, Brian Davies

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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.

Original language	English
Pages (from-to)	361-364
Number of pages	4
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	233
Issue number	4-6
DOIs	https://doi.org/10.1016/S0375-9601(97)00486-6
Publication status	Published - 1 Sept 1997

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AU - Batchelor, Murray T.

AU - Davies, Brian

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N2 - 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.

AB - 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.

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AN - SCOPUS:17844397113

SN - 0375-9601

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JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 4-6

ER -

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

Abstract

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