Specialized Interior Point Algorithm for Stable Nonlinear System Identification

TL;DR

This paper introduces a specialized interior point algorithm for stable nonlinear system identification that reduces computational complexity and improves generalization compared to existing methods.

Contribution

A novel path-following interior point algorithm exploiting problem structure, enabling efficient stable nonlinear system identification from large datasets.

Findings

Reduced computational complexity from cubic to linear growth.

Demonstrated superior generalization to new data.

Explored stability constraints as regularizers.

Abstract

Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation fidelity and guarantee stability via semidefinite programming (SDP), however the resulting SDPs have large dimension, limiting their utility in practical problems. In this paper we develop a path-following interior point algorithm that takes advantage of special structure in the problem and reduces computational complexity from cubic to linear growth with the length of the data set. The new algorithm enables empirical comparisons to established methods including Nonlinear ARX, and we demonstrate superior generalization to new data. We also explore the "regularizing" effect of stability constraints as an alternative to regressor subset selection.