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

Tidiane Diallo (1) , Dan Goreac (1)

1 PS

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.

Mots clés: backward stochastic Riccati difference scheme; controllability metric; linear decision process; null-controllability; gene networks; phage λ

Domaines: Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Tidiane Diallo, Dan Goreac. Controllability Metrics on Networks with Linear Decision Process-type Interactions and Multiplicative Noise. SIAM Journal on Control and Optimization, 2016, 54 (6), pp.3126-3151. ⟨10.1137/15M1043649⟩. ⟨hal-01214318v2⟩