Controllability Metrics on Networks with Linear Decision Process-type Interactions and Multiplicative Noise

Tidiane Diallo 1 Dan Goreac 1
1 PS
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
Abstract : This paper aims at the study of controllability properties and induced controllability metrics on complex networks governed by a class of (discrete time) linear decision processes with mul-tiplicative noise. The dynamics are given by a couple consisting of a Markov trend and a linear decision process for which both the " deterministic " and the noise components rely on trend-dependent matrices. We discuss approximate, approximate null and exact null-controllability. Several examples are given to illustrate the links between these concepts and to compare our results with their continuous-time counterpart (given in [16]). We introduce a class of backward stochastic Riccati difference schemes (BSRDS) and study their solvability for particular frameworks. These BSRDS allow one to introduce Gramian-like controllability metrics. As application of these metrics, we propose a minimal intervention-targeted reduction in the study of gene networks.
Type de document :
Article dans une revue
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2016, 54 (6), pp.3126-3151. 〈http://epubs.siam.org/doi/pdf/10.1137/15M1043649〉. 〈10.1137/15M1043649〉
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Dernière modification le : jeudi 11 janvier 2018 - 06:27:10
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Tidiane Diallo, Dan Goreac. Controllability Metrics on Networks with Linear Decision Process-type Interactions and Multiplicative Noise. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2016, 54 (6), pp.3126-3151. 〈http://epubs.siam.org/doi/pdf/10.1137/15M1043649〉. 〈10.1137/15M1043649〉. 〈hal-01214318v2〉

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