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Structural controllability of networks with dynamical nodes

Abstract : In this paper we consider networks which are governed by external controls. The internal nodes of the network are composed of linear dynamic systems, in such a way that the network graph is a static structure, while the life of the system is located in the nodes. Moreover, we assume that each node is a linear structured system with a single ingoing state vertex and a single outgoing state vertex. Recall that structured systems are dynamic systems where the entries of the corresponding state space matrices are independent parameters. To such structured systems, one can associate a directed graph that allows to study a lot of generic properties of the system. Combining the network graph with the node graphs provides with a global graph which will allow the study of the structural controllability of the global system. We give necessary and sufficient controllability conditions for the global system, with respect to the controllability of the nodes and to the properties of the network graph. The conditions are expressed in terms of an auxiliary graph which has the same size as the network graph, but takes into account important features of the node graphs. These conditions are particularly simple in the case where all the nodes have the same structure, and therefore the same graph. Besides its interest in terms of insight in the controllability of networks with dynamical nodes, this approach is also much more efficient computationally than a direct checking of the controllability of the global graph.
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https://hal.univ-grenoble-alpes.fr/hal-01806913
Contributor : Christian Commault <>
Submitted on : Monday, June 4, 2018 - 11:23:14 AM
Last modification on : Wednesday, October 7, 2020 - 11:34:17 AM
Long-term archiving on: : Wednesday, September 5, 2018 - 12:52:30 PM

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Christian Commault. Structural controllability of networks with dynamical nodes. 2018. ⟨hal-01806913⟩

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