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

TL;DR

This paper investigates controllability properties and metrics for complex networks modeled by discrete-time linear decision processes with multiplicative noise, introducing new Riccati schemes and applications to gene network reduction.

Contribution

It introduces a class of backward stochastic Riccati difference schemes and develops controllability metrics for networks with multiplicative noise, extending previous continuous-time results.

Findings

Defined approximate and null-controllability concepts.

Developed solvability conditions for BSRDS.

Applied metrics to gene network reduction.

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.