Desired group consensus in arbitrary signed networks

Abstract

This paper addresses the problem of achieving any desired group consensus in multi-agent systems (MAS) operating in arbitrary signed networks. By focusing on arbitrary network topologies, we develop a control strategy that drives the agents’ states towards any desired state, independent of initial conditions and network topology. Such a framework finds applications in targeted opinion formation in social networks to counter the spread of misinformation or opinion radicalization, spreading awareness through social media campaigns by governments or public health organizations, and in recommender systems. A key contribution is the introduction of a switching control mechanism that expands the range of reachable states, ensuring that any targeted outcome is attained for a given initial condition without imposing any constraints on the network structure. Our approach not only guarantees the formation of desired clusters but also ensures that each agent converges to the specified consensus value within its cluster. This gives a unified framework for addressing both the group as well as the scaled consensus problems. Mathematical analysis establishes conditions for achieving system stability and reachability to any desired state, based on which the control input is designed. Finally, the theoretical results are validated through numerical simulations on real-world and synthetic networks.