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Controlling chaos in high-dimensional systems. (English) Zbl 0964.37502
Summary: Recently formulated techniques for controlling chaotic dynamics face a fundamental problem when the system is high dimensional, and this problem is present even when the chaotic attractor is low dimensional. Here the authors introduce a procedure for controlling a chaotic time signal of an arbitrarily high dimensional system, without assuming any knowledge of the underlying dynamical equations. Then, the authors formulate a feedback control that requires modeling the local dynamics of only a single or a few of the possibly infinite number of phase-space variables.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37N99 Applications of dynamical systems
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