MATLAB functions

Network operations

Module framework

Name	Description
algebrloops	Evaluates the presence of algebraic loops in a network topology;
cannoise	Transforms a network to a canonical noise representation for a given set of measured nodes;
confvariables	Determines which signals $e$ act as confounding variable between two sets of $w$-nodes, for a given set of measured nodes, and specifies all corresponding confounding paths;
disconset4ppl	Determines a disconnecting set for satisfying the PPL condition for a particular target module;
immersion	Immerses a selected set of w-nodes in a network, including processing the properties: fixed, switching and delays;
invariantmodules	Shows all modules that are invariant when only a given set of measured nodes are taken into account, and the remaining nodes are immersed;
parpathlooptest	Tests whether for a given target module and a given set of measured nodes, the parallel path and loop condition is satisfied;

DCN framework

Name	Description
immersion_dcn	Immerses a selected set of w-nodes in a DCN network, including processing the properties: fixed, switching and delays;
invariantmodules_dcn	Shows all links in a DCN network that are invariant when only a given set of measured nodes are taken into account, and the remaining nodes are immersed;
parpathlooptest_dcn	Tests whether for a given target subnetwork and a given set of measured nodes, the parallel path and loop condition is satisfied;

Identifiability related operations

Module framework

Name	Description
modidfanalysis_fullm	Analyse the generic identifiability of a subset of modules in a dynamic network on the basis of full measurements of all nodes;
modidfanalysis_partial	Analyse the generic identifiability of a subset of modules in a dynamic network on the basis of a preselected set of measured nodes; R modules are assumed to be fixed. The test is based on a sufficient condition (Proposition 2 in Shi et al. (TAC-2023)).
modidfsynthesis	Allocates sensors and actuators such that the selected target modules become generically identifiable, where the inputs and outputs of the target modules will be measured; The allocated actuator dynamics are all known/fixed.
netwidfanalysis	Analysis whether a full network model set is generically identifiable;
netwidfsynthesis	Determines locations of external excitation signals for full network generic identifiability; algorithm of X. Cheng et al. (TAC-2022) in its extended form for dealing with fixed modules as published in M. Dreef et al. (L-CSS 2022).

DCN framework

Name	Description
modidfanalysis_dcn	Analyse the generic identifiability of a set of links in a DCN dynamic network model set;
modidfsynthesis_dcn	Allocates sensors and actuators such that a set of links in a DCN network becomes generically identifiable.
netwidfanalysis_dcn	Analysis whether a full DCN network model set is generically identifiable;
netwidfsynthesis_dcn	Allocates sensors and actuators for full DCN network generic identifiability.
subnetwidfanalysis_dcn	Analyse the generic identifiability of a subnetwork of a DCN dynamic network model set;
subnetwidfsynthesis_dcn	Allocates sensors and actuators such that the selected subnetwork becomes generically identifiable.

Predictor model related operations

Name	Description
construct_Tu	Given the structural properties (input and output nodes) of a predictor model, the matrix $T(q)$ is constructed, representing the mapping from external excitation signals u to predictor outputs.
datainform_analysis	For a given dynamic network topology, a target module and predictor model, it is tested whether it satisfies the generic data-informativity conditions of the target module for any of the identification methods.
datainform_analysis_dm_fullpm	For a given dynamic network topology, a target module and predictor model, it is tested whether it satisfies the generic data-informativity conditions of the full predictor model for the local direct method;
datainform_analysis_multistep_fullpm	For a given dynamic network topology, a target module and predictor model, it is tested whether it satisfies the generic data-informativity conditions of the full predictor model for the multistep method;
delaycond_analysis_dm	For a given dynamic network topology, a predictor model is tested whether it satisfies the delay conditions for consistent identification of a target module with the direct method.
predmodel_analysis_dm	Tests whether a given predictor model satisfies the (structural) conditions for consistent estimation of a single module with the direct method.
predmodel_analysis_multistep	Tests whether a given predictor model satisfies the (structural) conditions for consistent estimation of a single module with the multistep method.
predmodel_analysis_indirect	Tests whether a given predictor model satisfies the (structural) conditions for consistent estimation of a single module with the indirect method.
predmodel_syn_dm_fullinput	A predictor model is constructed that satisfies the structural conditions for consistent identification of a target module with the direct method. The structural conditions concern the parallel path and loop condition, and the absence of confounding variables. As option also the structural data-informativity conditions can be included. The ”fullinput” algorithm is followed to arrive at the choice of predictor model inputs and outputs. See Ramaswamy and Van den Hof (IEEE-TAC, 2021)
predmodel_syn_dm_mininput	Same function as the previous file, but now "the minimum input" algorithm is followed.
predmodel_syn_dm_usersel	Same function as the previous file, but now the "userselection" algorithm is followed.
predmodel_syn_dm_usersel2	Same function as the previous file, but now with the predictor model construction method of Shengling Shi (IFAC, 2023).
predmodel_syn_dm	Command-line file for running any of the four algorithms listed previously.
predmodel_syn multistep	Predictor model construction, but now with the predictor model construction method of the multi-step method (Fonken et al., CDC 2023).
predmodel_syn_indirect_fullm	Predictor model construction for the indirect method, full measurement case.
predmodel_addr	Adding the r-dependent input to a predictor model determined by predictor model inputs and outputs.
predmodel_addior	Adding the structural properties in terms of structured G, H and T to a predictor model for either the direct, multistep or indirect method, and deliver a predictor model in nwpredmodel class format.

Network data structures

Name	Description
LabelledAdjStruct	Network structure (topology) with all structural properties of the network.
nwdata	Data object to encapsulate node/excitation data of networked system and its properties.
nwpredmodel	Predictor model class, which specifies the mapping between nodes and excitations of a network structure to input and outputs of a predictor model.
nwmodel	Network model class: special case of the network predictor model class, in which all nodes and excitations are included.

Identification of directed / module networks

Name	Description
nwidfullSLS	Full network identification through a sequential Least-Squares (SLS) algorithm applied to an ARMAX mdel structure;
nwidPEM	Identification of a single module / full network through a (local) direct method;
nwidsingleMultiStep	Identification of a single module through a multi-step method;

Identification of undirected / diffusively coupled networks

Name	Description
nwidARMAX_dcn	Multi-step time-domain method for discrete-time DCN identfication;
nwidFreq_dcn	Multi-step frequency-domain method for discrete-time and continuous-time DCN identification;

Topology estimation (directed networks)

Name	Description
nwtopestBayes	Topology estimation with a Bayesian method;
nwtopevalBayes	Evaluation of an estimated topology with the Bayesian method;

Simulation

Name	Description
nwsimulate	Simulation of a directed / module or an undirected / DCN network;

Network conversions

Name	Description
slx2adj	Convert a Simulink file (.slx) to an adjacency matrix;

Specific technical functions for DCN models

Name	Description
adj2laplacian	Converts a 3d adjacency matrix to Laplacian
a2xy	Converts a (3d) polynomial matrix to diagonal and Laplacian term
diag3d	Extract the diagonal terms of a polynomial matrix
issymmetrix3d	Check if a polynomial matrix is symmetric
issymmetrictf	Check if a transfer function matrix is symmetric
laplacian2adj	Converts a 3d Laplacian matrix to an adjancency matrix
par2xy	Converts a coefficient vector into 3d polynomial matrices $X,Y$
poly2tf	Converts a polynomial matrix to tf format.
poly_d2c	Converts a DT polynomial matrix (in $q^{-1})$ into a CT form (in $p$)
poly_c2d	Converts a CT polynomial matrix (in $p$) into a CT form (in $q^{-1}$)
xy2par	Converts polynomial matrices $X,Y$ to a coefficient vector

Technical tasks

Name	Description
blockedpaths	Verify whether all paths between a single node and a set of nodes are blocked by a specified set of blocking nodes.
confseqeunce	Determines whether there exists a sequence of linked confounders between two nodes in a network.
delaycheck	For a given dynamic network topology and the delay properties of each module in G, it is verified whether all paths from nodes in one set to the nodes in another set have at least a delay. This file works with negative delays also.
disconset_analysis	Verfy whether a given set is a disconnecting set between two specified node sets.
EsourcesForExcitation	Determine which $e$-nodes can be used as sources for exciting inputs in a predictor model.
existunmeasuredpath	Test whether there exists a direct or unmeasured path between two sets of nodes.
mindismaxpath	Determines a minimum disconnecting set and a maximum number of vertex disjoint paths between two sets of nodes;
nodeselect	For a set of vectors of node numbers, a (minimal) selection of nodes is chosen such that for each vector at least one member is included. The algorithm can either provide a (nonunique) solution or provide options for the user to choose from.
numberofinstruments	Finds the number of independent instrumentations for a given excitation and measurement setup.
predmodel_separateAB	For the ($w$-) inputs and outputs of a predictor model, separate the inputs in sets $A$ and $B$, according to the confounding variable condition for consistent estimation (direct method);
unblockedpaths	Construct all paths between two specified single nodes that are not blocked by a specified set of blocking nodes.
unmeasuredpath	Finds a direct or unmeasured path between each pair of nodes in two node sets;