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Identifiability Window

In the Identifiability window the generic identifiability of a specified structured network is evaluated of which the topology is known. Generic identifiability is considered for a network class where all unknown modules/links are freely parametrized and all known modules/links are fixed. Generic identifiability concerns the property that a network or module can uniquely be retrieved from the information that is available. It is typically dependent on

  • the presence and location of external excitation signals rr;
  • the topology (interconnection structure) of the network;
  • the presence of known modules;
  • the selection of node variables that are considered to be available for the identifiability study; typically these are the measured node variables.

Generic identifiability of a full network and of a single module can be investigated. In the latter situation a target module needs to be selected either using the dropdown in the Network panel, or by clicking on the module in the network plot.

Measurements Full/Partial​

Identifiability studies consider ALL present node signals to be available (selected), or allows the specification of a selection of node signals, whose information will be used for the identifiability studies. When choosing "Partial Measurement" a new panel is opened that allows to select the set of node signals. These signals can also be selected/deselected by clicking on the nodes in the network plot.

Analysis​

An analysis is made of the generic identifiability of the chosen object. A yes/no answer is displayed through the Pass/fail lamp.

Synthesis​

The generic identifiability of the network/module is analyzed and if not satisfied a suggestion is made where to add external excitation signals or additionally measured nodes (in the partial measurement case), so as to realize generic identifiability.

In the full network case, the synthesis problem is addressed by covering the network graph with disjoint pseudotrees, and to guarantee that every pseudotree is excited in one of its roots by an external signal, either a disturbance process e or a measured external excitation signal rr. A pseudotree is a rooted tree or a cycle with outgoing trees. In the latter situation any of the nodes in the cycle acts as a root. If there are multiple options for adding excitations, the user can select one of them, or leave the selection to the algorithm. If known modules are present the pseudotree covering is replaced by a covering with SIMUGs (single-source identifiable multi-rooted graphs), which allow the most effective exploitation of known modules in the network (see Ref. 5). In a SIMUG the maximum number of parametrized incoming edges of a node does not exceed 1.

Add/remove excitation signals​

Given the importance of the presence and location of external excitation signals rr for identifiability properties, this panel allows to add/delete external excitation signals as part of the workflow on identifiability studies.

Algorithm restrictions​

The identifiability algorithms accomodate for known modules; they can not treat switching modules, those are considered as known modules. The algorithms can fully deal with the situation of reduced rank disturbance processes (nonsquare HH). The single module synthesis algorithm is currently only applicable to networks of small size (< 20 nodes).

References​

The implemented algorithms result from the following publications:

  1. H.H.M. Weerts, P.M.J. Van den Hof and A.G. Dankers. Single module identifiability in linear dynamic networks. Proc. 57th IEEE Conf. Decision and Control, 17-19 December 2018, Miami Beach, FL, pp. 4725-4730.
  2. 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.
  3. 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.
  4. 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.
  5. 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.