The Control of high-dimensional Chaos in Time-Delay Systems

Details The Control of high-dimensional Chaos in Time-Delay Systems The Control of high-dimensional Chaos in Time-Delay Systems

1999-05-03

arxiv.org/abs/chao-dyn/9905003v1

Nonlinear Sciences

Chaotic Dynamics

6 pages, 4 figures, accepted for publication in 'Chaos'

Scientific paper

We present the control of the high-dimensional chaos, with possibly a large number of positive Lyapunov-exponents, of unknown time-delay systems to an arbitrary goal dynamics. We give an existence-and-uniqueness theorem for the control force. In the case of an unknown system, a formula to compute a model-based control force is derived. We give an example by demonstrating the control of the Mackey-Glass system towards a fixed point and a R\"ossler-dynamics.

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