TY - JOUR
T1 - Stability borders of feedback control of delayed measured systems
AU - Claussen, Jens Christian
PY - 2004/10/19
Y1 - 2004/10/19
N2 - When stabilization of unstable periodic orbits or fixed points by the method given by Ott, Grebogi, and Yorke (OGY) must be based on a measurement delayed by τ orbit lengths, the performance of unmodified OGY method is expected to decline. For experimental considerations, it is desired to know the range of stability with minimal knowledge of the system. We find that unmodified OGY control fails beyond a maximal Lyapunov number of λmax=1+(1∕τ). In this paper the area of stability is investigated both for OGY control of known fixed points and for difference control of unknown or inaccurately known fixed points. An estimated value of the control gain is given. Finally we outline what extensions must be considered if one wants to stabilize fixed points with Lyapunov numbers above λmax.
AB - When stabilization of unstable periodic orbits or fixed points by the method given by Ott, Grebogi, and Yorke (OGY) must be based on a measurement delayed by τ orbit lengths, the performance of unmodified OGY method is expected to decline. For experimental considerations, it is desired to know the range of stability with minimal knowledge of the system. We find that unmodified OGY control fails beyond a maximal Lyapunov number of λmax=1+(1∕τ). In this paper the area of stability is investigated both for OGY control of known fixed points and for difference control of unknown or inaccurately known fixed points. An estimated value of the control gain is given. Finally we outline what extensions must be considered if one wants to stabilize fixed points with Lyapunov numbers above λmax.
UR - http://www.scopus.com/inward/record.url?scp=37649028709&partnerID=8YFLogxK
UR - https://journals.aps.org/pre/abstract/10.1103/PhysRevE.70.046205
U2 - 10.1103/PhysRevE.70.046205
DO - 10.1103/PhysRevE.70.046205
M3 - Article
AN - SCOPUS:37649028709
SN - 1539-3755
VL - 70
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 4
M1 - 046205
ER -