Identification of diffusively coupled linear networks through structured polynomial models

@article{Kivits2022IdentificationOD,
  title={Identification of diffusively coupled linear networks through structured polynomial models},
  author={E.M.M. Kivits and Paul M. J. Van den Hof},
  journal={IEEE Transactions on Automatic Control},
  year={2022}
}
—Physical dynamic networks most commonly consist of interconnections of physical components that can be described by diffusive couplings. These diffusive couplings imply that the cause-effect relationships in the interconnections are symmetric and therefore physical dynamic networks can be represented by undirected graphs. This paper shows how prediction error identification methods developed for linear time-invariant systems in polynomial form can be configured to consistently identify the… 

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References

SHOWING 1-10 OF 40 REFERENCES
Revealing network connectivity from response dynamics.
  • M. Timme
  • Mathematics
    Physical review letters
  • 2007
TLDR
This work considers networks of coupled phase oscillators and explicitly study their long-term stationary response to temporally constant driving, finding good predictions of the actual connectivity even for formally underdetermined problems.
Allocation of Excitation Signals for Generic Identifiability of Linear Dynamic Networks
TLDR
The proposed approach can be adapted using the notion of antipseudotrees to solve a dual problem, which is to select a minimal number of measurement signals for generic identifiability of the overall network, under the assumption that all the vertices are excited.
Identifiability of Dynamical Networks With Partial Node Measurements
TLDR
This paper presents the first results for the situation where not all node signals are measurable, under the assumptions that, first, the topology of the network is known, and, second, each node is excited by a known external excitation.
Reduction of Second-Order Network Systems With Structure Preservation
TLDR
This paper proposes a general framework for structure-preserving model reduction of a second-order network system based on graph clustering, and develops an efficient method to compute inline-formula-norms and derive the approximation error between the full-order and reduced-order models.
Identification of dynamic networks operating in the presence of algebraic loops
TLDR
It is shown that the classical one-step-ahead predictor that incorporates direct feedt-hrough terms in models can not be used in a dynamic network setting and has to be replaced by a network predictor, for which consistency results are shown when applied in a direct identification method.
Subspace Identification of Large-Scale Interconnected Systems
TLDR
It is proved that the state of a local subsystem can be approximated by a linear combination of inputs and outputs of local subsystems that are in its neighborhood, and that for interconnected systems with well-conditioned, finite-time observability Gramians, the size of this neighborhood is relatively small.
Dynamical structure functions for the reverse engineering of LTI networks
TLDR
Dynamical structure functions are introduced as an alternative, graphical-model based representation of LTI systems that contain both dynamical and structural information of the system.
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