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

Mert Ankarali, Johns Hopkins University
Dec 12 2014 - 1:00pm
Event type: 
Applied Dynamical Systems
122 Lewis Library

Few tools exist for identifying the dynamics of rhythmic systems from input–output data. This paper inves- tigates 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.