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Frequency-Domain Analysis and Design of Distributed Control Systems by Yu-Ping Tian

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Chapter 6

Consensus in Homogeneous Multi-Agent Systems

Like seeks to like, and (birds) of the same note respond to one another –this is a rule of Heaven.

—Zhuang Zi (368–286 BC), ‘The Old Fisherman'

Cooperation is a central topic in the design of a distributed control system. One of the most convenient and efficient approaches to undertaking a cooperative task for the agents of a distributed control system is to achieve some agreement (consensus). This chapter introduces basic notions in consensus problems, such as consensus protocol, the existence of consensus solutions and consentability. A unified approach to treating the consensus problem as a stability problem is presented. The consensus problem for systems with homogeneous agents of the first order, second order and nth order is investigated.

6.1 Introduction to Consensus Problem

In this section we introduction some basic notions in consensus problems by considering a simple multi-agent system: a system with integrator agents over an ideal network, i.e., a network without communication delays.

6.1.1 Integrator Agent System

Consider a multi-agent system with a fixed topology digraph G = (V, E, A). Each agent can be considered as a node in the digraph, and an information flow between two agents can be regarded as a directed path between two nodes. Each dynamic agent is described by

(6.1) equation

where and , and . The control ui adopts ...

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