Containment Control Approach for Steering Opinion in a Social Network

The paper studies the problem of steering multi-dimensional opinions in a social network. We assume that the society of interest consists of stubborn and regular agents, where stubborn agents act as leaders who define the desired opinion distribution through a distributed reward or utility function. In this framework, each regular agent is treated as a follower that updates its bias on the initial opinion and adjusts its influence weights by averaging the observed rewards received by its influencers. Considering random graphs with both reducible and irreducible topologies to model the influences on regular agents, the opinion evolution is formulated as a containment control problem, where stability and convergence to the final opinion are established.