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.
Complete list of metadatas

https://hal-upec-upem.archives-ouvertes.fr/hal-01214318
Contributor : Admin Lama <>
Submitted on : Wednesday, December 14, 2016 - 11:29:49 AM
Last modification on : Friday, October 4, 2019 - 1:14:07 AM
Long-term archiving on : Wednesday, March 15, 2017 - 1:43:49 PM

Files

GoreacDiallo_CtrlMetrics_Rev_1...
Files produced by the author(s)

Identifiers

Citation

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. ⟨10.1137/15M1043649⟩. ⟨hal-01214318v2⟩

Share

Metrics

Record views

283

Files downloads

311