An optimal gains matrix for time-delay feedback control

James Biggs; Colin R. McInnes

doi:10.3182/20090622-3-UK-3004.00063

An optimal gains matrix for time-delay feedback control

James Biggs, Colin R. McInnes

Mechanical And Aerospace Engineering

Research output: Contribution to conference › Paper

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Abstract

In this paper we propose an optimal time-delayed feedback control (TDFC) for tracking unstable periodic orbits (UPOs). It is shown that TDFC will drive a trajectory onto a periodic orbit while minimising an integral of a cost function of the error in periodicity and the control e®ort. This optimal TDFC relies on the linearisation about the delayed trajectory not the UPO itself and therefore can be implemented without a priori knowledge of a reference orbit. This optimal TDFC is applied to the problem of tracking an unstable periodic orbit in the nonlinear equations describing the circular restricted three-body problem. The results of this investigation demonstrate that TDFC could e±ciently drive a spacecraft onto a periodic orbit in the vicinity of a (UPO) halo orbit.

Original language	English
Number of pages	4
DOIs	https://doi.org/10.3182/20090622-3-UK-3004.00063
Publication status	Published - 22 Jun 2009
Event	2nd IFAC Conference on the Analysis and Control of Chaotic Systems (CHAOS 09) - London, England Duration: 22 Jun 2009 → 24 Jun 2009

Conference

Conference	2nd IFAC Conference on the Analysis and Control of Chaotic Systems (CHAOS 09)
City	London, England
Period	22/06/09 → 24/06/09

Keywords

feedback control
chaos theory
control systems
orbits
periodic orbits

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10.3182/20090622-3-UK-3004.00063

strathprints007755Accepted author manuscript, 384 KB

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Cite this

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title = "An optimal gains matrix for time-delay feedback control",

abstract = "In this paper we propose an optimal time-delayed feedback control (TDFC) for tracking unstable periodic orbits (UPOs). It is shown that TDFC will drive a trajectory onto a periodic orbit while minimising an integral of a cost function of the error in periodicity and the control e{\textregistered}ort. This optimal TDFC relies on the linearisation about the delayed trajectory not the UPO itself and therefore can be implemented without a priori knowledge of a reference orbit. This optimal TDFC is applied to the problem of tracking an unstable periodic orbit in the nonlinear equations describing the circular restricted three-body problem. The results of this investigation demonstrate that TDFC could e±ciently drive a spacecraft onto a periodic orbit in the vicinity of a (UPO) halo orbit.",

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AU - McInnes, Colin R.

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N2 - In this paper we propose an optimal time-delayed feedback control (TDFC) for tracking unstable periodic orbits (UPOs). It is shown that TDFC will drive a trajectory onto a periodic orbit while minimising an integral of a cost function of the error in periodicity and the control e®ort. This optimal TDFC relies on the linearisation about the delayed trajectory not the UPO itself and therefore can be implemented without a priori knowledge of a reference orbit. This optimal TDFC is applied to the problem of tracking an unstable periodic orbit in the nonlinear equations describing the circular restricted three-body problem. The results of this investigation demonstrate that TDFC could e±ciently drive a spacecraft onto a periodic orbit in the vicinity of a (UPO) halo orbit.

AB - In this paper we propose an optimal time-delayed feedback control (TDFC) for tracking unstable periodic orbits (UPOs). It is shown that TDFC will drive a trajectory onto a periodic orbit while minimising an integral of a cost function of the error in periodicity and the control e®ort. This optimal TDFC relies on the linearisation about the delayed trajectory not the UPO itself and therefore can be implemented without a priori knowledge of a reference orbit. This optimal TDFC is applied to the problem of tracking an unstable periodic orbit in the nonlinear equations describing the circular restricted three-body problem. The results of this investigation demonstrate that TDFC could e±ciently drive a spacecraft onto a periodic orbit in the vicinity of a (UPO) halo orbit.

KW - feedback control

KW - chaos theory

KW - control systems

KW - orbits

KW - periodic orbits

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T2 - 2nd IFAC Conference on the Analysis and Control of Chaotic Systems (CHAOS 09)

Y2 - 22 June 2009 through 24 June 2009

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