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Small force control of nonlinear systems to given orbits

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4 Author(s)
Abarbanel, H.D.I. ; Dept. of Phys., California Univ., San Diego, La Jolla, CA, USA ; Korzinov, L. ; Mees, A. ; Rulkov, N.F.

Using a low frequency nonlinear electrical circuit, we experimentally demonstrate an efficient nonlinear control method based on our theoretical developments. The method works in a state space for the circuit which is reconstructed from observations of a single voltage. Assuming small control variations from the uncontrolled state, the method is fully nonlinear and “one step” optimal. It requires no knowledge of Local state space linearizations of the dynamics near the target state. Starting from various initial states within the basin of attraction of the circuit attractor, we control to a period one and to a period two target orbit. Each target orbit is an unstable periodic orbit of the uncontrolled system

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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:44 ,  Issue: 10 )