Stable Nonlinear Identification From Noisy Repeated Experiments via Convex Optimization

TL;DR

This paper develops convex optimization methods for stable nonlinear system identification from noisy repeated experiments, ensuring consistent and stable models without input-output data assumptions.

Contribution

It introduces a novel convex optimization approach for stable nonlinear model identification that leverages repeated experiments to mitigate noise effects.

Findings

Convex optimization scheme guarantees stable model estimates.

Repeated experiments effectively reduce noise influence.

Method demonstrated successfully on simulated data.

Abstract

This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small set of repeated experiments with suitably independent measurement noise is available. Stability of the estimated models is guaranteed without any assumptions on the input-output data. We first present a convex optimization scheme for identifying stable state-space models from empirical moments. Next, we provide a method for using repeated experiments to remove the effect of noise on these moment and model estimates. The technique is demonstrated on a simple simulated example.