Title: Convex Parameterizations and Fidelity Bounds for Nonlinear Identification and Reduced-Order Modelling,
Abstract: Model instability and poor prediction of long-term behavior are common
problems when modeling dynamical systems using nonlinear "black-box"
techniques. Direct optimization of the long-term predictions, often called
simulation error minimization, leads to optimization problems that are
generally non-convex in the model parameters and suffer from multiple local
minima. In this work we present methods which address these problems through
convex optimization, based on Lagrangian relaxation, dissipation inequalities,
contraction theory, and semidefinite programming. We demonstrate the proposed
methods with a model order reduction task for electronic circuit design and the
identification of a pneumatic actuator from experiment.