Nonlinear state-space identification using deep encoder networks

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Nonlinear state-space identification for dynamical systems is most often performed by minimizing the simulation error to reduce the effect of model errors. This optimization problem becomes computationally expensive for large datasets. Moreover, the problem is also strongly non-convex, often leading to sub-optimal parameter estimates. This paper introduces a method that approximates the simulation loss by splitting the data set into multiple independent sections similar to the multiple shooting method. This splitting operation allows for the use of stochastic gradient optimization methods which scale well with data set size and has a smoothing effect on the non-convex cost function. The main contribution of this paper is the introduction of an encoder function to estimate the initial state at the start of each section. The encoder function estimates the initial states using a feed-forward neural network starting from historical input and output samples. The efficiency and performance of the proposed state-space encoder method is illustrated on two well-known benchmarks where, for instance, the method achieves the lowest known simulation error on the Wiener--Hammerstein benchmark.
Original languageEnglish
Title of host publicationProceedings of Learning for Dynamics and Control, 7-8 June 2021, The Cloud
EditorsAli Jadbabaie, John Lygeros, George J. Pappas
Number of pages10
Publication statusPublished - 2021
Event3rd Annual Conference on Learning for DynamIcs & Control, L4DC 2021 - Zurich, Switzerland
Duration: 7 Jun 20218 Jun 2021
Conference number: 3

Publication series

NameProceedings of Machine Learning Research
ISSN (Print)2640-3498


Conference3rd Annual Conference on Learning for DynamIcs & Control, L4DC 2021
Abbreviated titleL4DC 2021
Internet address


  • Nonlinear System Identification
  • Deep Learning
  • State-Space
  • Multiple Shooting


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