(386h) Latent Dynamic Networked System Identification with High-Dimensional Data from Interconnected Process Networks

Networked dynamic systems produce high-dimensional data that reflect the complex
interactions among the network nodes with rich sensor measurements. These
systems are composed of interconnected nodes with their own dynamics and dynamic
interactions with other nodes [1, 2]. The nodes in the networked systems are often
equipped with a rich set of sensors that yield high-dimensional time series data.
Recent works have dealt with the estimation and system identification problems of
these networked models with tremendous progress [3, 4, 5]. However, in dealing with
high-dimensional networked systems data, little has been done in extracting low-
dimensional latent dynamic networks from the high-dimensional networked data [6].

In this paper, we propose a novel algorithm for latent dynamic networked system
identification that leverages the network structure and performs dimension reduction
for each node via dynamic latent variables (DLVs). The algorithm assumes that
the DLVs of each node have an auto-regressive model with exogenous input and
interactions from other nodes. The DLVs of each node are extracted to capture
the most predictable latent variables in the high dimensional data, while the residual
factors are not predictable. The advantage of the proposed framework is demonstrated
on an industrial process network for system identification and dynamic data analytics
and are summarized as follows.
1) To handle co-moving or collinear dynamics, low dimensional dynamics is captured
on each individual node system to extract DLVs with a network topology;
2) The DLVs of each node are vector auto-regressive with exogenous input (VARX)
and dynamic connections to other nodes following a given topology;
3) The proposed framework extends single-node DLV methods to networked dynamic
systems to analyze high-dimensional networked time series data.
4) The identified network model is a networked latent VARX model (Net-LaVARX),
which is readily suitable for networked system identification.

References

[1] X. Wang and H. Su, “Pinning control of complex networked systems: A decade
after and beyond,” Annual Reviews in Control, vol. 38, no. 1, pp. 103–111, 2014.
[2] T. Zhou, K. You, and L. Tao, Estimation and Control of Large-Scale Networked
Systems. Elsevier Science, 2018.
[3] A. G. Dankers, P. M. Van den Hof, and P. S. Heuberger, “Predictor input selection
for direct identification in dynamic networks,” in 52nd IEEE Conference on
Decision and Control. IEEE, 2013, pp. 4541–4546.
[4] M. Zamani, B. Ninness, and J. C. Ag¨uero, “On identification of networked systems
with time-invariant topology,” IFAC-PapersOnLine, vol. 48, no. 28, pp. 1184–
1189, 2015, 17th IFAC Symposium on System Identification SYSID 2015.
[5] A. Haber and M. Verhaegen, “Subspace identification of large-scale interconnected
systems,” IEEE Transactions on Automatic Control, vol. 59, no. 10, pp. 2754–
2759, 2014.
[6] S. J. Qin, Y. Dong, Q. Zhu, J. Wang, and Q. Liu, “Bridging systems theory and
data science: A unifying review of dynamic latent variable analytics and process
monitoring,” Annual Reviews in Control, vol. 50, pp. 29–48, October 2020.