Specialized Interior-Point Algorithm for Stable Nonlinear System Identification

Estimation of nonlinear dynamic models from data poses many challenges, including model instability and nonconvexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation fidelity and guarantee stability via semidefinite programming...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 64; no. 6; pp. 2442 - 2456
Main Authors: Umenberger, Jack, Manchester, Ian R.
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Autoregressive models
Computational modeling
Computer simulation
Data models
Dynamic models
Dynamic stability
Dynamical systems
Mathematical model
Nonlinear dynamics
Nonlinear system identification
Nonlinear systems
optimization algorithms
Predictive models
Semidefinite programming
Stability analysis
stability of nonlinear systems
State-space methods
System identification
ISSN:0018-9286, 1558-2523, 1558-2523
Online Access:Get full text
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Summary:Estimation of nonlinear dynamic models from data poses many challenges, including model instability and nonconvexity 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 dataset. The new algorithm enables empirical comparisons to established methods including nonlinear autoregressive models with exogenous inputs, and we demonstrate superior generalization to new data. We also explore the "regularizing" effect of stability constraints as an alternative to regressor subset selection.
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ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2018.2867358