Specialized Interior-Point Algorithm for Stable Nonlinear System Identification

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.

Distributed Identification of Contracting and/or Monotone Network Dynamics

“…Some approaches, e.g., [26], [27], effectively fix the stability certificate, but this can be conservative even for linear systems. This paper builds on previous work in jointly-convex parameterization of models and their stability certificates via implicit models [28], [29], [30], [31], [32], [33] and associated convex bounds for model fidelity via Lagrangian relaxation [31], [34], [35].…”

“…It has be previously noted that system identification approaches that guarantee stability lead to a bias towards systems that are too stable [21], [22], [72]. Empirical evidence suggests that for methods based on Lagrangian relaxation [34], [35] this bias is smaller.…”

Integrated neuro-swarm heuristic with interior-point for nonlinear SITR model for dynamics of novel COVID-19

“…Therefore, an operative local search IPA is used for adjustment of the results based on the proposed optimization. Recently, IPA is used in active noise control models [34] , simulation of aircraft parts riveting [35] , mixed model of complementary monotone [36] , economic load dispatch classification [37] and nonlinear identification models [38] . The present study is to present the solutions through the hybridization of PSOIPA to solve the SITR nonlinear mathematical model.…”

A neuro-swarming intelligent heuristic for second-order nonlinear Lane–Emden multi-pantograph delay differential system

“…Therefore, a rapid and operative local search approach based on interior-point (IP) algorithm is implemented to adjust the solutions attained by the designed optimization algorithm. Few recent submissions of the IP algorithm are active noise control systems [53], mixed complementarity monotone systems [54], simulation of aircraft parts riveting [55], nonlinear system identification [56] and economic load dispatch model [57].…”