Search

Equation error, also known as one-step-ahead prediction error, is a common quality-of-fit metric in dynamical system identification and learning. In this letter, we use Lagrangian relaxation to construct a convex upper bound on equation error that can be optimized over a convex set of nonlinear models that are guaranteed to be contracting, a strong form of nonlinear stability. We provide theoretical results on the tightness of the relaxation, and show that the method compares favorably to established methods on a variety of case studies.

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.

A new framework for nonlinear system identification is presented in terms of optimal fitting of stable nonlinear state space equations to input/output/state data, with a performance objective defined as a measure of robustness of the simulation error with respect to equation errors. Basic definitions and analytical results are presented. The utility of the method is illustrated on a simple simulation example as well as experimental recordings from a live neuron., National Science Foundation (U.S.). (Grant number 0835947)