Switching Transformations for Decentralized Control of Opinion Patterns in Signed Networks: Application to Dynamic Task Allocation

Abstract

We propose a new decentralized design 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 the interactions with its neighbors. The global dynamical behavior of the switched network can be predicted rigorously when the original, and thus the switched, 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 monotone systems theory. We illustrate the utility of the approach through scenarios motivated by multi-robot coordination and dynamic task allocation. Index Terms-Network analysis and control, distributed control, agents-based systems, control of networks, decentralized control. I. INTRODUCTIONM ODERN networked technologies require decentralized mechanisms for decision-making and allocation of tasks. For example, systems such as smart power grids, cloud computing services, or multi-robot teams, call for strategies that dynamically distribute tasks among individual units to optimize system performance even as task requirements change or units experience failure.

Fast and Flexible Multiagent Decision-Making

“…If the opinion dynamics are monotone (67,95), then m = 1. Monotonicity can be guaranteed in the case of structurally balanced network interactions (96)(97)(98).…”

“…Characterizations of both the pitchfork and Hopf bifurcations have appeared in various works (36,58,91,98,99,(101)(102)(103)(104)(105)(106)(107)(108)(109) with varying assumptions about the structure of the communication and belief system networks and damping coefficients. In the cases studied, the critical and sensitivity subspaces of the bifurcation coincide with eigenspaces of standard graph matrices-e.g., the graph Laplacian L (36,91,(101)(102)(103)(104)(105) or communication adjacency matrix A a (98, 99, 106-108)for two options and with the product of adjacency matrices of communication and belief system graphs A a ࣹ A o in the general case (58,(107)(108)(109).…”

Opinion-Driven Robot Navigation: Human-Robot Corridor Passing

“…Opinion dynamics have been used to facilitate collective decision-making in robotic teams [17]- [19]. In the present paper, we use opinion dynamics to drive the social navigation of a robot interacting with a human.…”