Asymptotic consensus and asymptotic group consensus of Boolean networks with additive noise

Abstract

This paper solves the asymptotic consensus problem and asymptotic group consensus problem of Boolean networks (BNs) with additive noise disturbance. Firstly, the definition of asymptotic consensus of BNs is proposed. Secondly, the algebraic state space presentation of BNs is described by identifying node states in BNs as canonical forms and using basic knowledge of semi-tensor product of matrices (STP). Thirdly, two kinds of additive noises are considered by converting the dynamics of BNs into a discrete-time stochastic system and two necessary and sufficient conditions are correspondingly proposed. An illustrative example is implemented to verify the obtained theoretical results. Finally, as an extension of asymptotic consensus problem, the asymptotic group consensus problem with additive noises is studied.