Consensus of Discrete-Time Linear Multi-Agent Systems with Observer-Type Protocols

TL;DR

This paper introduces observer-type protocols for discrete-time multi-agent systems with linear dynamics, analyzing their consensus regions and providing algorithms to ensure consensus under various stability conditions, with applications to formation control.

Contribution

It proposes novel observer-type protocols for discrete-time multi-agent systems, characterizes their consensus regions, and offers algorithms for achieving consensus across different communication topologies.

Findings

Consensus can be achieved with protocols having a bounded region in the unit disk.

Existence of protocols with consensus regions as origin-centered disks of radius δ.

Algorithms are provided for stabilizable and detectable agents to reach consensus.

Abstract

This paper concerns the consensus of discrete-time multi-agent systems with linear or linearized dynamics. An observer-type protocol based on the relative outputs of neighboring agents is proposed. The consensus of such a multi-agent system with a directed communication topology can be cast into the stability of a set of matrices with the same low dimension as that of a single agent. The notion of discrete-time consensus region is then introduced and analyzed. For neurally stable agents, it is shown that there exists an observer-type protocol having a bounded consensus region in the form of an open unit disk, provided that each agent is stabilizable and detectable. An algorithm is further presented to construct a protocol to achieve consensus with respect to all the communication topologies containing a spanning tree. Moreover, for the case where the agents have no poles outside the unit circle,an algorithm is proposed to construct a protocol having an origin-centered disk of radius $\delta$ ($0<\delta<1$) as its consensus region, where $\delta$ has to further satisfy a constraint related to the unstable eigenvalues of a single agent for the case where each agent has a least one eigenvalue outside the unit circle. Finally, the consensus algorithms are applied to solve formation control problems of multi-agent systems.