# Convex Parameterizations and Fidelity Bounds for Nonlinear Identification and Reduced-Order Modelling

## TL;DR

This paper introduces convex optimization methods for nonlinear system identification and model reduction, improving stability and long-term prediction accuracy by leveraging Lagrangian relaxation, dissipation inequalities, and semidefinite programming.

## Contribution

It presents novel convex optimization techniques for nonlinear system modeling, addressing non-convexity and local minima issues in traditional approaches.

## Key findings

- Effective model order reduction for electronic circuits.
- Successful pneumatic actuator identification from experimental data.
- Enhanced stability and long-term prediction accuracy.

## 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.