• Corpus ID: 212736902

Unifying Theorems for Subspace Identification and Dynamic Mode Decomposition

@article{Shin2020UnifyingTF,
  title={Unifying Theorems for Subspace Identification and Dynamic Mode Decomposition},
  author={Sungho Shin and Qiugang Lu and Victor M. Zavala},
  journal={ArXiv},
  year={2020},
  volume={abs/2003.07410}
}
This paper presents unifying results for subspace identification (SID) and dynamic mode decomposition (DMD) for autonomous dynamical systems. We observe that SID seeks to solve an optimization problem to estimate an extended observability matrix and a state sequence that minimizes the prediction error for the state-space model. Moreover, we observe that DMD seeks to solve a rank-constrained matrix regression problem that minimizes the prediction error of an extended autoregressive model. We… 

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References

SHOWING 1-10 OF 21 REFERENCES
Optimal low-rank Dynamic Mode Decomposition
  • P. Héas, C. Herzet
  • Computer Science
    2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
  • 2017
TLDR
This paper proves that there exists a closed-form optimal solution to this problem and design an effective algorithm to compute it based on Singular Value Decomposition (SVD), and illustrates the gain in performance of the proposed algorithm compared to state-of-the-art techniques.
Dynamic Mode Decomposition with Control
TLDR
This work develops a new method which extends dynamic mode decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models.
Low-Rank Dynamic Mode Decomposition: Optimal Solution in Polynomial-Time
TLDR
There exists a closed-form solution to the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition, which can be computed in polynomial-time, and characterises the l2-norm of the optimal approximation error.
Canonical variate analysis in identification, filtering, and adaptive control
  • W. Larimore
  • Mathematics
    29th IEEE Conference on Decision and Control
  • 1990
The canonical variate analysis (CVA) approach for system identification, filtering, and adaptive control is developed. The past/future Markov property provides a starting point for defining a
Identification of State-Space Models from Time and Frequency Data
TLDR
This dissertation considers the identication of linear multivariable systems using finite dimensional time-invariant state-space models using vibrational analysis of mechanical structures and introduces a new model quality measure, Modal Coherence Indicator, and new multivariables frequency domain identification algorithms.
On dynamic mode decomposition: Theory and applications
TLDR
A theoretical framework in which dynamic mode decomposition is defined as the eigendecomposition of an approximating linear operator, which generalizes DMD to a larger class of datasets, including nonsequential time series, and shows that under certain conditions, DMD is equivalent to LIM.
N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems
Dynamic mode decomposition - data-driven modeling of complex systems
TLDR
This first book to address the DMD algorithm presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development, and blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses.
Subspace state space system identification for industrial processes
Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator
TLDR
This work establishes the convergence of a class of numerical algorithms, known as dynamic mode decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator, and shows that the singular value decomposition, which is the central part of most DMD algorithms, converges to the proper orthogonal decomposition of observables.
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