Parametric adaptive control and parameter identification of low-dimensional chaotic systems

Abstract The presented method of adaptive control corrects perturbations in the parameters of a system based on observations of its variables. After a transient during which the desired parameter setting is reached exponentially quickly, the system exhibits the goal behavior - which can be a periodic, quasiperiodic, or chaotic solution of the equations of motion. The length of the control transient scales inversely with the control strength and logarithmically with the magnitude of the original parameter perturbation. It is shown that time series-based models are capable of substituting for detailed knowledge of the system's nonlinear dynamics. The method can be generalized to control more than one parameters, to rely on observations of a single variable, or to utilize a variety of control functions. Finally, a method of parameter identification dual to the adaptive control is also discussed.

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