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An optimal gains matrix for time-delay feedback control

Biggs, J.D. and McInnes, C.R. (2009) An optimal gains matrix for time-delay feedback control. In: 2nd IFAC Conference on the Analysis and Control of Chaotic Systems (CHAOS 09), 2009-06-22 - 2009-06-24.

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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.