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

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.

References in corpus (4)

• On Submodularity and Controllability in Complex Dynamical Networks
• Backward stochastic differential equation driven by a marked point process: An elementary approach with an application to optimal control
• Approximate Controllability for Linear Stochastic Differential Equations in Infinite Dimensions
• Algebraic Invariance Conditions in the Study of Approximate (Null-)Controllability of Markov Switch Processes