Continuous-time min-max consensus protocol: A unified approach

In this paper, a new consensus protocol is designed for linear agents in the presence of a time variant communication topology. Furthermore, we aim to present a fully distributed unified consensus protocol. Using the proposed protocol, each agent within a communication network can iteratively update its state to the maximum state of its neighbors, change it to the minimum state of the neighboring agents, or keep its state constant. In contrast to conventional consensus protocols, which strongly require the weights of communication graph links to have a positive lower bound for reaching consensus, our proposed protocol is not restricted by such a requirement and is able to make the agents converge under more general conditions. To accelerate the convergence rate and reduce the computational time relative to other conventional protocols, various operating modes (i.e., Tracker, Following, and Cross) are assigned to each agent within the communication network. Finally, to prove the practical merits of the proposed protocol and validate its performance, two numerical examples are presented here, one for a consensus problem, and another for a consensus-based formation problem.