Fixed-time consensus algorithm for multi-agent systems with integrator dynamics

International audienceThe paper addresses the problem of exact average-consensus reaching in a prescribed time. The communication topology is assumed to be defined by a weighted undirected graph and the agents are represented by integrators. A nonlinear control protocol, which ensures a finite-time convergence, is proposed. With the designed protocol, any prescribed convergence time can be guaranteed regardless of the initial conditions

Network science on belief system dynamics under logic constraints

Breakthroughs have been made in algorithmic approaches to understanding how individuals in a group influence each other to reach a consensus. However, what happens to the group consensus if it depends on several statements, one of which is proven false? Here, we show how the existence of logical constraints on beliefs affect the collective convergence to a shared belief system and, in contrast, how an idiosyncratic set of arbitrarily linked beliefs held by a few may become held by many

A new model of opinion dynamics for social actors with multiple interdependent attitudes and prejudices

Unlike many complex networks studied in the literature, social networks rarely exhibit regular cooperative behavior such as synchronization (referred usually as consensus or agreement of the opinions). This requires a development of mathematical models that capture the complex behavior of real social groups, where opinions and the actions related to them form clusters of different size, and yet are sufficiently simple to be examined. One such model, proposed in [1], deals with scalar opinions and extends the idea in [2] of iterative pooling in a way to take into account the actors’ prejudices, caused by some exogenous factors and leading to disagreement in the final opinions. In this paper, we offer two extensions, where opinions are multidimensional, representing the agents’ attitudes on several topics, and those topic-specific attitudes are interrelated. We examine convergence of the proposed model and find explicitly the steady opinions of the agents. Although our model assumes synchronous communication among the agents, we show that the same final opinion may be achieved “on average” via asynchronous randomized gossip-based protocol

Network science on belief system dynamics under logic constraints.

Breakthroughs have been made in algorithmic approaches to understanding how individuals in a group influence each other to reach a consensus. However, what happens to the group consensus if it depends on several statements, one of which is proven false? Here, we show how the existence of logical constraints on beliefs affect the collective convergence to a shared belief system and, in contrast, how an idiosyncratic set of arbitrarily linked beliefs held by a few may become held by many