Chaotification via arbitrarily small feedback controls: theory, method, and applications. (English) Zbl 1090.37532

Summary: The problem of making a stable nonlinear autonomous system chaotic or enhancing the existing chaos of an originally chaotic system by using a small-amplitude feedback controller is studied. The designed controller is a linear feedback controller composed with a nonlinear modulo or sawtooth function, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, thereby yielding chaotic dynamics. We mathematically prove that the controlled system is indeed chaotic in the sense of Li and Yorke. A few potential applications of the new chaotification algorithm are briefly discussed.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
93B52 Feedback control
93C55 Discrete-time control/observation systems
Full Text: DOI


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