1 research outputs found
Sensitivity Analysis for Hybrid Systems and Systems with Memory
We present an adjoint sensitivity method for hybrid discrete -- continuous
systems, extending previously published forward sensitivity methods. We treat
ordinary differential equations and differential-algebraic equations of index
up to two (Hessenberg) and provide sufficient solvability conditions for
consistent initialization and state transfer at mode switching points, for both
the sensitivity and adjoint systems. Furthermore, we extend the analysis to
so-called hybrid systems with memory where the dynamics of any given mode
depend explicitly on the states at the last mode transition point. We present
and discuss several numerical examples, including a computational mechanics
problem based on the so-called exponential model constitutive material law for
steel reinforcement under cyclic loading