Min-Consensus for Heterogeneous Higher-Order Integrators Under Switching Digraph

Abstract

For a multi-agent system (MAS), researchers have explored min-consensus for single-integrators under uniformly strongly-connected digraph, and double-integrators under jointly-connected graphs. However, the extension of these works is non-trivial for heterogeneous higher-order integrators under switching digraphs. This letter proposes a min-consensus protocol for MAS with higher-order integrators under uniformly strongly-connected digraph. The protocol consists of a distributed observer and a decentralized tracking controller. Each agent distributively estimates the minimum of initial values of all agents by using its neighbors’ information only. The decentralized controller ensures that the agents follow their respective estimated values. This structure of the protocol allows a set of heterogeneous higher-order integrators to achieve min-consensus. Theoretical proofs and numerical simulations validate the proposed min-consensus protocol. Through numerical example, we also establish that a group of heterogeneous integrators cannot achieve min-consensus, in general, without a uniformly strongly-connected digraph.