Data-Driven Koopman Operator Approximations for Piezoelectric Composites with Hysteresis

Abstract

This dissertation addresses the modeling and prediction of hysteretically nonlinear piezo- electric composite beams. Three primary contributions are made. First, a first-principles modeling framework is developed that formulates the coupled piezoelectric hysteresis system as a functional differential equation using the Assumed Mode Method with a Krasnosel'skii- Pokrovskii hysteresis operator, validated against a direct finite element model. Second, novel error bounds are derived for data-driven Koopman operator approximations in vector- valued reproducing kernel Hilbert spaces, explicitly decomposing the total prediction error into sample and approximation error terms. Third, an adaptive greedy kernel center se- lection strategy is developed that directly targets the approximation error term, achieving significant reductions in model complexity and improved robustness to measurement noise.