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Dynamical singularities in adaptive delayed-feedback control
1Future University Hakodate, 116-2 Kameda Nakano-cho, Hakodate, Hokkaido 041-8655, Japan. saito@fun.ac.jp
Abstract:
We demonstrate the dynamical characteristics of adaptive delayed-feedback control systems, exploiting a discrete-time adaptive control method derived for carrying out detailed analysis. In particular, the systems exhibit singularities such as power-law decay of the distribution of transient times and almost zero finite-time Lyapunov exponents. We can explain these results by characterizing such systems as having (1) a Jacobian matrix with unity eigenvalue in the whole phase space, and (2) parameters approaching a stability boundary proven to be identical with that of (nonadaptive) delayed-feedback control.
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