The adaptive control of a simple chaotic system to a steady reference is investigated. An indirect adaptive control scheme with least-mean-squares (LMS) parameter estimation yields a fractal basin boundary between stable and unstable control. This boundary appears self-similar, indicative of a fractal structure, and has a fractal dimension of 2.61. Adaptive control using a least-squares (LS) estimator appears globally stable with the rate of adaptation a complex function of the distance from the desired set point. The effect of control parameters, noise and a step-change perturbation of the system are also reported.

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