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System Identification of Rhythmic Hybrid Dynamical Systems via Discrete Time Harmonic Transfer Functions

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2014-12-17
Ankaralı, Mustafa Mert
Cowan, Noah J.
Few tools exist for identifying the dynamics of rhythmic systems from input-output data. This paper investigates the system identification of stable, rhythmic hybrid dynamical systems, i. e. systems possessing a stable limit cycle but that can be perturbed away from the limit cycle by a set of external inputs, and measured at a set of system outputs. By choosing a set of Poincare sections, we show that such a system can be (locally) approximated as a linear discrete-time periodic system. To perform input-output system identification, we transform the system into the frequency domain using discrete-time harmonic transfer functions. Using this formulation, we present a set of stimuli and analysis techniques to recover the components of the HTFs nonparametrically. We demonstrate the framework using a hybrid spring-mass hopper. Finally, we fit a parametric approximation to the fundamental harmonic transfer function and show that the poles coincide with the eigenvalues of the Poincare return map.