Consensus in Heterogeneous Higher-Order Agents Driven by Geometric Mean under Weight-Unbalanced Digraph

This paper proposes a distributed algorithm to drive all agents in a heterogeneous multi-agent system (MAS) to the geometric mean of their initial conditions. It is defined as the GM-consensus problem. The proposed GM-consensus algorithm has a distributed observer for estimating the geometric mean of agents' initial states. Its later part is a local controller for tracking these observed states. This structure facilitate the scaling of the algorithm for the agents having higher-order model. The numerical example exemplifies the efficiency of the proposed distributed GM-consensus algorithm.