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

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.