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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.
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Preprints, Working Papers, ...
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https://hal-upec-upem.archives-ouvertes.fr/hal-01214318
Contributor : Dan Goreac Connect in order to contact the contributor
Submitted on : Monday, October 12, 2015 - 2:10:05 AM
Last modification on : Tuesday, October 19, 2021 - 4:09:57 PM
Long-term archiving on: : Wednesday, January 13, 2016 - 11:01:25 AM

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GoreacDiallo_CtrlMetrics.pdf
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Identifiers

  • HAL Id : hal-01214318, version 1
  • ARXIV : 1510.03157

Citation

Tidiane Diallo, Dan Goreac. Controllability Metrics on Networks with Linear Decision Process-type Interactions and Multiplicative Noise. 2015. ⟨hal-01214318v1⟩

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Metrics

Les métriques sont temporairement indisponibles