Sensitivity Analysis for Hybrid Systems and Systems with Memory
This work provides a theoretical and computational framework for sensitivity analysis in hybrid systems, which is important for optimization and control in engineering domains like mechanics.
The paper presents an adjoint sensitivity method for hybrid discrete-continuous systems, extending forward sensitivity methods, and applies it to systems with memory, demonstrated on a computational mechanics problem.
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.