An optimal gains matrix for time-delay feedback control

James Biggs, Colin R. McInnes

Research output: Contribution to conferencePaperpeer-review

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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 languageEnglish
Number of pages4
Publication statusPublished - 22 Jun 2009
Event2nd IFAC Conference on the Analysis and Control of Chaotic Systems (CHAOS 09) - London, England
Duration: 22 Jun 200924 Jun 2009


Conference2nd IFAC Conference on the Analysis and Control of Chaotic Systems (CHAOS 09)
CityLondon, England


  • feedback control
  • chaos theory
  • control systems
  • orbits
  • periodic orbits

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