Decentralised Probabilistic Consensus Control for Stochastic Complex Dynamical Networks

This letter is concerned with the consensus analysis and control problems for a class of stochastic complex dynamical networks (SCDNs) that consists of a large number of interconnected nodes. In particular, a unified probabilistic decentralised consensus control framework is established where decentralised randomised controllers are designed such that the individual subsystems in a network synchronise their states with each other to achieve consensus of the whole network. The proposed framework is quite general, where all the components within this framework including local controllers, systems' models, and communications between the subsystems of a complex system are modelled using probabilistic models. The general solution for arbitrary probabilistic models of the framework components is obtained then demonstrated on a class of linear Gaussian complex systems, thus obtaining the desired results. Furthermore, a numerical example is presented to illustrate the effectiveness and the usefulness of the theoretical development.