TY - JOUR
T1 - Linear and optimal non-linear control of one-dimensional maps
AU - McGuire, Justin
AU - Batchelor, Murray T.
AU - Davies, Brian
PY - 1997/9/1
Y1 - 1997/9/1
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.
UR - http://www.scopus.com/inward/record.url?scp=17844397113&partnerID=8YFLogxK
U2 - 10.1016/S0375-9601(97)00486-6
DO - 10.1016/S0375-9601(97)00486-6
M3 - Article
AN - SCOPUS:17844397113
SN - 0375-9601
VL - 233
SP - 361
EP - 364
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 -