SOCN Course Network Identification – 2026

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Identification in dynamic networks

VUB Brussels, March 4-6, 2026

Lecturer:

Prof. Paul Van den Hof, TU/e, Eindhoven
Date of the course: 4 – 6 March 2026.
VUB, Brussels, Belgium.

MATLAB App and Toolbox

Most methods presented in this course have been implemented in the MATLAB App and Toolbox SYSDYNET with graphical and interactive user interface. It can be downloaded from www.sysdynet.net. Please check to work with release Beta 0.4.0 (2025), available from xxx, x 2025 onwards.

Summary

In many areas of science and technology, the complexity of dynamic systems that are being considered, grows beyond the level of single systems. Current challenges move to the monitoring, diagnostics, control and optimization of interconnected systems, represented as dynamic networks. In control and optimization this has led to the development of decentralized and distributed algorithms for control/optimization, as e.g. present in multi-agent systems. From the modelling perspective, data-driven modelling challenges lie in the processing of high-dimensional data, exploiting the ubiquitous availability of sensor data, and turning measurement data into dynamic and structured information on the causal relationships between the different nodes (sensor signals) in the network. As a further generalization of the closed-loop identification problem, network identification problems have to face and exploit the structure of the interconnections between different components in the network.

In this course we will highlight the main developments and challenges in this area. Besides setting up a modelling framework for both directed (transfer function based) and non-directed (equation based) networks, we will address problems of local identification of a particular part of the network, including the selection of the appropriate signals to be measured, and the selection of excitation signals. The concept of network identifiability is highlighted and the role of structural properties of the network, in terms of its topology/graph, is given strong attention. It is also shown how classical closed-loop identification methods need to be generalized to be able to cope with the new situations, leading to a variation of appropriate algorithms. Examples will be shown through the MATLAB App and Toolbox SYSDYNET that will be made available to the attendees.

The schedule below is only tentative.

Wednesday March 4, 2026

09:30 – 12:30:

13:50 – 16:30

Network identifiability – Analysis
Network identifiability – Synthesis
Full module network identification
Matlab App and Toolbox SYSDYNET (demo)

Thursday March 5, 2026

09:30 – 12:30

13:50 – 16:30

Friday March 6, 2026

09:30 – 12:30

Diffusively coupled networks
Modeling and identifiability

13:50 – 16:30

Full network and subnetwork identification
Algorithms
Discussion and reflection

Background material

Closed-loop identification:

Chapter 10 in Lecture notes: “System Identification – Data-driven Modeling of Dynamic Systems”, Paul M.J. Van den Hof, Version February 2020.

Dynamic networks:

P.M.J. Van den Hof, A. Dankers, P. Heuberger and X. Bombois (2013). Identification of dynamic models in complex networks with prediction error methods – basic methods for consistent module estimates. Automatica, Vol. 49, no. 10, pp. 2994-3006.
E.M.M. Kivits and P.M.J. Van den Hof (2018). On representations of linear dynamic networks. IFAC PapersOnLine, Vol. 51-15, pp. 838-843. Proc. 18th IFAC Symposium on System Identification (SYSYD 2018), 9-11 July 2018, Stockholm, Sweden.

Network identifiability analysis:

H.H.M. Weerts, P.M.J. Van den Hof and A.G. Dankers (2018). Identifiability of linear dynamic networks. Automatica, Vol. 89, pp. 247-258, March 2018.
J. M. Hendrickx, M. Gevers and A.S. Bazanella (2019). Identifiability of dynamical networks with partial node measurements. IEEE Trans. Automatic Control, Vol. 64, no. 6, pp. 2240-2253.

Network identifiability synthesis:

X. Cheng, S. Shi and P.M.J. Van den Hof (2022). Allocation of excitation signals for generic identifiability of linear dynamic networks. IEEE Trans. Automatic Control, Vol. 67, no. 2, pp. 692-705, February 2022.
H.J. Dreef, S. Shi, X. Cheng, M.C.F. Donkers and P.M.J. Van den Hof (2022). Excitation allocation for generic identifiability of linear dynamic networks with fixed modules. IEEE Control Systems Letters (L-CSS), Volume 6, pp. 2587-2592.

Algorithms for full network identification:

H.H.M. Weerts, P.M.J. Van den Hof and A.G. Dankers (2018). Prediction error identification of linear dynamic networks with rank-reduced noise. Automatica, Vol. 98, pp. 256-268, December 2018.
H.H.M. Weerts, M. Galrinho, G. Bottegal, H. Hjalmarsson and P.M.J. Van den Hof (2018). A sequential least squares algorithm for ARMAX dynamic network identification. IFAC PapersOnLine, Vol. 51-15, pp. 844-849. Proc. 18th IFAC Symposium on System Identification (SYSYD 2018), 9-11 July 2018, Stockholm, Sweden.
S.J.M. Fonken, K.R. Ramaswamy and P.M.J. Van den Hof (2022). A scalable multi-step least squares method for network identification with unknown disturbance topology. Automatica,Volume 141 (110295), July 2022.

Single module identification:

A. Dankers, P.M.J. Van den Hof, X. Bombois and P.S.C. Heuberger (2016). Identification of dynamic models in complex networks with predictior error methods – predictor input selection. IEEE Trans. Automatic Control, Vol. 61, no. 4, pp. 937-952.
K.R. Ramaswamy, P.M.J. Van den Hof and A.G. Dankers. Generalized sensing and actuation schemes for local module identification in dynamic networks. Proc. 58th IEEE Conf. Decision and Control, Nice, France, 11-13 December 2019, pp. 5519-5524.
K.R. Ramaswamy, G. Bottegal and P.M.J. Van den Hof (2021). Learning linear models in a dynamic network using regularized kernel-based methods. Automatica, Vol. 129 (109591), July 2021.
K.R. Ramaswamy and P.M.J. Van den Hof (2021). A local direct method for module identification in dynamic networks with correlated noise. IEEE Trans. Automatic Control, Vol. 66, no. 11, pp. 3237-3252, November 2021.
V.R. Rajagopal, K.R. Ramaswamy and P.M.J. Van den Hof (2021). Learning local modules in dynamic networks without prior topology information. Proc. 60th IEEE Conf. Decision and Control, December 13-15, 2021, Austin, TX, USA, pp. 840-845.
S.J.M. Fonken, K.R. Ramaswamy and P.M.J. Van den Hof (2023). Local identification in dynamic networks using a multi-step least squares method. Proc. 62nd IEEE Conf. Decision and Control,13-15 December 2023, Marina Bay Sands, Singapore, pp. 431-436.

Data-informativity

P.M.J. Van den Hof and K.R. Ramaswamy (2020). Path-based data-informativity conditions for single module identification in dynamic networks. Proc. 59th IEEE Conf. Decision and Control, Jeju Island, Republic of Korea, 15-18 December 2020, pp. 4354-4359.
X. Bombois, K.Colin, P.M.J. Van den Hof and H. Hjalmarsson. On the informativity of direct identification experiments in dynamical networks. Automatica, Vol. 148 (110742), February 2023.
P.M.J. Van den Hof, K.R. Ramaswamy and S.J.M. Fonken (2023). Integrating data-informativity conditions in predictor models for single module identification in dynamic networks. IFAC PapersOnLine, Vol. 56-2 (2023), pp. 2377-2382.Proc. 22nd IFAC World Congress, 9-14 July 2023, Yokohama, Japan.

Single module identifiability:

S. Shi, X. Cheng and P.M.J. Van den Hof (2022). Generic identifiability of subnetworks in a linear dynamic network: the full measurement case. Automatica, Vol. 117 (110093), March 2022.
S. Shi, X. Cheng and P.M.J. Van den Hof (2023). Single module identifiability in linear dynamic networks with partial excitation and measurement. IEEE Trans. Automatic Control, Vol. 68, no. 1, pp. 285-300, January 2023.

Relation with diffusively coupled physical networks:

E.M.M. Kivits and P.M.J. Van den Hof (2019). A dynamic network approach to identification of physical systems. Proc. 58th IEEE Conf. Decision and Control, Nice, France, 11-13 December 2019, pp. 4533-4538.
E.M.M. Kivits and P.M.J. Van den Hof (2023). Identification of diffusively coupled linear networks through structured polynomial models. IEEE Trans. Automatic Control, Vol. 68, no. 6, pp. 3513-3528, June 2023.