论文信息 - On the stability of delayed feedback control of chaos

On the stability of delayed feedback control of chaos

Limitations in controlling chaos in continuous dynamical systems by delayed feedback are proved. The results are as follows: (1) If the linear variational equation about a hyperbolic unstable periodic orbit (UPO) has an odd number of real characteristic multipliers which are greater than unity, the UPO can never be stabilized with any value of feedback gain. (2) If all the characteristic exponents of the variational equation are different from each other and at least one of them is real and positive, then the UPO can never be stabilized with any feedback gain matrix of the form of diag(k, ..., k). These theorems are proved on the basis of Floquet theory. The result of the first theorem is also explained intuitively using bifurcation theory.

H. Nakajima | Y. Ueda | Y. Ueda | H. Nakajima

[1] Takashi Hikihara,et al. An experimental study on stabilization of unstable periodic motion in magneto-elastic chaos , 1996 .

[2] Joshua E. S. Socolar,et al. Stability of periodic orbits controlled by time-delay feedback , 1995, chao-dyn/9510019.

[3] Kestutis Pyragas. Continuous control of chaos by self-controlling feedback , 1992 .

[4] T. Ushio. Limitation of delayed feedback control in nonlinear discrete-time systems , 1996 .

[5] Keiji Konishi,et al. Control of chaotic systems using an on-line trained linear neural controller , 1997 .

[6] Kestutis Pyragas. Control of chaos via extended delay feedback , 1995 .

[7] Glorieux,et al. Controlling unstable periodic orbits by a delayed continuous feedback. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.