Modeling and sensitivity analysis methodology for hybrid dynamical systems

TL;DR

This paper introduces an analytical sensitivity analysis methodology for second order hybrid ODE systems with impulsive impacts, enabling precise parameter sensitivity computations in systems with discontinuities.

Contribution

It presents a novel analytical approach for computing sensitivities in hybrid dynamical systems with impacts, benchmarked against numerical methods.

Findings

The analytical method accurately computes sensitivities in hybrid systems.

The approach handles discontinuities due to impacts effectively.

Benchmark results show improved efficiency over numerical methods.

Abstract

This paper provides an analytical methodology to compute the sensitivities with respect to system parameters for any second order hybrid Ordinary Differential Equation (ODE) system. The hybrid ODE system is characterized by discontinuities in the velocity state variables due to an impulsive jump caused by an instantaneous impact in the motion of the system. The analytical methodology that solves this problem is structured based on jumping conditions for both the state variables and the sensitivities matrix. The proposed analytical approach is of the benchmarked against a numerical method.