Parameter Identification Near Periodic Orbits of Hybrid Dynamical Systems

We present a novel identification framework that enables the use of first-order methods when estimating model parameters near a periodic orbit of a hybrid dynamical system. The proposed method reduces the space of initial conditions to a smooth manifold that contains the hybrid dynamics near the periodic orbit while maintaining the parametric dependence of the original hybrid model. First-order methods apply on this subsystem to minimize average prediction error, thus identifying parameters for the original hybrid system. We implement the technique and provide simulation results for a hybrid model relevant to terrestrial locomotion.