Uncertainty Quantification in Hybrid Dynamical Systems

Uncertainty quantification (UQ) techniques are frequently used to ascertain output variability in systems with parametric uncertainty. Traditional algorithms for UQ are either system-agnostic and slow (such as Monte Carlo) or fast with stringent assumptions on smoothness (such as polynomial chaos and Quasi-Monte Carlo). In this work, we develop a fast UQ approach for hybrid dynamical systems by extending the polynomial chaos methodology to these systems. To capture discontinuities, we use a wavelet-based Wiener-Haar expansion. We develop a boundary layer approach to propagate uncertainty through separable reset conditions. The above methods are demonstrated on example problems.