http://dadun.unav.edu/bitstream/10171/2018/1/2000.PhysRep.pdf

The control of chaos: theory and applications

Control of multistability

Control of chaos: Methods and applications in engineering

The problems and methods of control of chaos, which in the last decade was the subject of intensive studies, were reviewed. The three historically earliest and most actively developing directions of research such as the open-loop control based on periodic system excitation, the method of Poincare map linearization (OGY method), and the method of time-delayed feedback (Pyragas method) were discussed in detail. The basic results obtained within the framework of the traditional linear, nonlinear, and adaptive control, as well as the neural network systems and fuzzy systems were presented. The open problems concerned mostly with support of the methods were formulated. The second part of the review will be devoted to the most interesting applications.

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Control of Chaos: Methods and Applications. I. Methods

The CNN Paradigm for Complexity

We report theoretical and experimental results on the stabilization of unstable steady states in a CO2 laser with feedback. Periodic and chaotic oscillations have been suppressed by means of a control loop consisting of a high-pass filter, known as washout filter. Although the filter characteristics are determined on the basis of linear analysis, taking into account the problem of robustness with respect to parameter changes, the present control strategy provides a large attractive domain in the phase space.

Stabilization of unstable fixed points in the dynamics of a laser with feedback.

Experimental evidence of selection and stabilization of spatial patterns in a CO2 laser by means of spatial perturbations

In this paper we present a control technique for stabilizing chaotic motion to periodic orbits in a ${\mathrm{CO}}_{2}$ laser with electro-optic feedback. The control method is based on negative feedback of subharmonic components of the laser intensity signal. A detailed analysis, performed using the four-level model for the ${\mathrm{CO}}_{2}$ laser, allows us both to reproduce the experimental features and to compare our method with the time-delayed autosynchronization method introduced by Pyragas [Phys. Lett. A 170, 421 (1992)].

Controlling chaos by negative feedback of subharmonic components

Controlling quasiperiodicity in a CO 2 laser with delayed feedback

We introduce a novel control method for a delayed dynamical system exhibiting high-dimensional chaos. The control is based on a negative feedback loop with an adaptive filtering, consisting of a selective filter, centered at the frequency of the orbit to be stabilized, with the addition of a time derivative correction. The validity of the method is also discussed in the framework of a space-like representation adopted to study the analogies between delayed dynamical systems and spatially extended systems.

A. Labate

Papers

Stabilization of unstable fixed points in the dynamics of a laser with feedback.

Experimental evidence of selection and stabilization of spatial patterns in a CO2 laser by means of spatial perturbations

Controlling chaos by negative feedback of subharmonic components

Controlling quasiperiodicity in a CO 2 laser with delayed feedback

Experimental control of chaos in a delayed high-dimensional system