On the smoothness of nonlinear system identification

Antônio H. Ribeiro (Corresponding author), Koen Tiels, Jack Umenberger, Thomas B. Schön, Luis A. Aguirre

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

Abstract

We shed new light on the smoothness of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems. We show that for regions of the parameter space where the model is not contractive, the Lipschitz constant and β-smoothness of the objective function might blow up exponentially with the simulation length, making it hard to numerically find minima within those regions or, even, to escape from them. In addition to providing theoretical understanding of this problem, this paper also proposes the use of multiple shooting as a viable solution. The proposed method minimizes the error between a prediction model and the observed values. Rather than running the prediction model over the entire dataset, multiple shooting splits the data into smaller subsets and runs the prediction model over each subset, making the simulation length a design parameter and making it possible to solve problems that would be infeasible using a standard approach. The equivalence to the original problem is obtained by including constraints in the optimization. The new method is illustrated by estimating the parameters of nonlinear systems with chaotic or unstable behavior, as well as neural networks. We also present a comparative analysis of the proposed method with multi-step-ahead prediction error minimization.
Original languageEnglish
Article number109158
Number of pages15
JournalAutomatica
Volume121
DOIs
Publication statusPublished - Nov 2020

Keywords

  • Multiple shooting
  • Output error models
  • Parameter estimation
  • Prediction error methods
  • System identification

Fingerprint Dive into the research topics of 'On the smoothness of nonlinear system identification'. Together they form a unique fingerprint.

Cite this