The single-input Minimal Controllability Problem for structured systems

Christian Commault 1 Jean-Michel Dion 1
1 GIPSA-SLR - SLR
GIPSA-DA - Département Automatique
Abstract : This paper considers the Minimal Controllability Problem (MCP), {\em i.e.} the problem of controlling a linear system with an input vector having as few non-zero entries as possible. We focus on structured systems which represent an interesting class of parameter dependent linear systems and look for structural controllability properties based on the sparsity pattern of the input vector. We show first that the MCP is solvable when a rank condition is satisfied and show that generically one non-zero entry in the input vector is sufficient to achieve controllability when there is no specific system structure. According to the fixed zero/non-zero pattern of the state matrix entries, we give an explicit characterisation of the minimum number and the possible location of non-zero entries in the input vector to ensure generic controllability. The analysis based on graph tools provides with a simple polynomial MCP solution and highlights the structural mechanisms that make it useful to act on some variables to ensure controllability.
Type de document :
Article dans une revue
Systems and Control Letters, Elsevier, 2015, 80, pp.50-55. 〈10.1016/j.sysconle.2015.03.010〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01154379
Contributeur : Christian Commault <>
Soumis le : jeudi 21 mai 2015 - 17:40:20
Dernière modification le : vendredi 15 septembre 2017 - 16:13:32

Identifiants

Collections

Citation

Christian Commault, Jean-Michel Dion. The single-input Minimal Controllability Problem for structured systems. Systems and Control Letters, Elsevier, 2015, 80, pp.50-55. 〈10.1016/j.sysconle.2015.03.010〉. 〈hal-01154379〉

Partager

Métriques

Consultations de la notice

139