Nuclear norm-enhanced recursive subspace identification: Closed-loop estimation of rapid variations in system dynamics

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5 Citations (Scopus)


For a time-varying plant operating in closed-loop with a stabilising controller, rapid changes in system dynamics can be detected online using recursive subspace identification methods to estimate the open-loop system behaviour. However, these methods usually involve a speed-accuracy trade-off: accurate identification can often only be achieved by slow updates, which increases the lag in the detection of changes in system dynamics. In this paper, a closed-loop, recursive subspace identification algorithm is extended with a convex cost function based on the nuclear norm. The nuclear norm heuristic exploits structure in the algorithm by enforcing a low-rank condition on the state predictor matrix. This condition reduces the variance of the estimates at the price of introducing a bias. The new algorithm is demonstrated for a system where the damping changes from positive to negative, and it is shown to successfully and consistently estimate the onset of open-loop instability, outperforming conventional recursive identification. Further, by tuning the forgetting factor in the estimation algorithm, a favourable speed-accuracy trade-off can be achieved.
Original languageEnglish
Title of host publicationProceedings of the 2016 American Control Conference (ACC 2016)
EditorsGeorge Chiu, Katie Johnson, Danny Abramovitch
Place of PublicationPiscataway, NJ, USA
ISBN (Print)978-1-4673-8682-1
Publication statusPublished - 2016
EventAmerican Control Conference (ACC), 2016 - Boston, MA, United States
Duration: 6 Jul 20168 Jul 2016


ConferenceAmerican Control Conference (ACC), 2016
Abbreviated titleACC 2016
Country/TerritoryUnited States
CityBoston, MA


  • Cost function
  • Markov processes
  • Estimation
  • System dynamics
  • Heuristic algorithms
  • Minimization


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