# IEEE Proceedings Paper on Concensus and Cooperative Control

Consensus and Cooperation in Multi-Agent Networked Systems

The availability of low cost, high bandwidth, wireless communications between independent computing systems has enabled new approaches to cooperation between multi-agent systems performing a common task. In situations where the tasks involve motion control or other non-trivial process dynamics, the overall stability and performance of the cooperative system is dependent on the interaction between the topology of the information flow between the agents (who talks to who) as well as the individual dynamics of the agents. In this paper we explore two representative problems---consensus and formation control---and their applications in control of networked, multi-vehicle systems performing cooperative tasks.

Consensus refers to the problem of a set of distributed computers agreeing on some common quantity. The simplest version of this problem, which we call average consensus, requires the agents to agree on the average value of a set of quantities that are known to each individual agent. In vehicle applications, this often must be done in the presence of varying information topology, for example when a collection of robots are trying to agree on the position of a sensed object while moving and changing the topology of their wireless network connections. We present a framework for studying the concensus problems that models the information flow using the graph Laplacian and gives a provably correct consensus protocol in the presence of switching topology and delays.

Using the same graph theoretic methods, we also consider the the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. We provide a Nyquist-like criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the graph on formation stability. We also demonstrate how to use concensus to improve the performance of the system, by supplying each vehicle with a common reference to be used for cooperative motion. A separation principle that states that formation stability is achieved if the information flow is stable for the given graph and if the local controller stabilizes the vehicle. The information flow can be rendered highly robust to changes in the graph, thus enabling tight formation control despite limitations in intervehicle communication capability.

I. Introduction and Motivation

II. Basic Tools

III. Consensus

IV. Cooperation

V. Future Directions

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## Topics

1. Nyquist/Laplacian ] Fiedeler vectors -> decomposition 2. Consensus/balanced graphs ] of multi-agent groups 3. Switching (incl. Ali, Moreau) ] 4. Performance (lambda_2, feedfwd, etc) 5. Distributed information processing 6. Tools: graph theory, stochastic matrices, Lyapunov 7. Asynchronous consensus (Mesbahi) 8. Alignment in flocking (proximity graphs, post-induced graphs)

## Actions

1. Assemble bibliography

* Send papers to Richard by Mon, 5 pm * Post to wiki (Demetri)

2. Pick subset to cover ] Meet in ~2 weeks 3. Common notation/language ] 18 Apr 4. Common problems ]

5. List tools ] Meet in ~2 weeks 6. Diversions/open problems ] 6 May 7. Outline ]

8. Write ] Finish by 6/15/05

Compelling benchmark problem

* perhaps something that might be mobile sensor network