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

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Ankarali M. M. , Cowan N. J.

53rd IEEE Annual Conference on Decision and Control (CDC), Los-Angeles, Chile, 15 - 17 December 2014, pp.1017-1022 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.1109/cdc.2014.7039515
  • City: Los-Angeles
  • Country: Chile
  • Page Numbers: pp.1017-1022
  • Middle East Technical University Affiliated: No


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.