Input and State Observability of Network Systems with Time-Varying Topology

Sebin Gracy 1 Federica Garin 1 Alain Y. Kibangou 1
1 NECS-POST - Systèmes Commandés en Réseau
Inria Grenoble - Rhône-Alpes, GIPSA-DA - Département Automatique
Abstract : We aim to study the problem of reconstructing the initial state as well as the sequence of unknown inputs (ISO) for linear network systems having time-varying topology. Evolution of such systems can be represented by a collection of graphs {G k }. We find conditions under which the system with a pattern of fixed zeros imposed by {G k } is ISO: a) for almost all choices of edge weights in {G k } (structural ISO); and b) for all non-zero choices of edge weights in {G k } (strongly structural ISO). We introduce two suitable descriptions of the whole collection of graphs {G k } named as dynamic graph and dynamic bipartite graph. Two equivalent characterizations of structural ISO are then stated in terms of existence of a linking and a matching of suitable size in the dynamic graph and in the dynamic bipartite graph, respectively. For strongly structural ISO, we provide a sufficient condition and a necessary condition, both concerning the existence of a uniquely restricted matching of suitable size in the dynamic bipartite graph and in a subgraph of it. When there is no direct feedthrough of the input on the measurements, the two conditions can be merged to give rise to a necessary and sufficient condition.
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Sebin Gracy, Federica Garin, Alain Y. Kibangou. Input and State Observability of Network Systems with Time-Varying Topology. IEEE Transactions on Control of Network Systems, IEEE, In press, pp.1-9. ⟨10.1109/TCNS.2018.2880304⟩. ⟨hal-01918497⟩

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