Switching transformations for decentralized control of opinion patterns in signed networks: application to dynamic task allocation

We propose a new decentralized design method to control opinion patterns on signed networks of agents making decisions about two options and to switch the network from any opinion pattern to a new desired one. Our method relies on switching transformations, which switch the sign of an agent's opinion at a stable equilibrium by flipping the sign of its local interactions with its neighbors. The global dynamical behavior of the switched network can be predicted rigorously when the original, and thus the witched, networks are structurally balanced. Structural balance ensures that the network dynamics are monotone, which makes the study of the basin of attraction of the various opinion patterns amenable to rigorous analysis through monotone systems theory. We illustrate the utility of the approach through scenarios motivated by multi-robot coordination and dynamic task allocation.