A survey on distributed estimation and control applications using linear consensus algorithms

In this chapter we present a popular class of distributed algorithms, known as linear consensus algorithms, which have the ability to compute the global average of local quantities. These algorithms are particularly suitable in the context of multi-agent systems and networked control systems, \textit{i.e.}\ control systems that are physically distributed and cooperate by exchanging information through a communication network. We present the main results available in the literature about the analysis and design of linear consensus algorithms,for both synchronous and asynchronous implementations. We then show that many control, optimization and estimation problems such as least squares, sensor calibration, vehicle coordination and Kalman filtering can be cast as the computation of some sort of averages, therefore being suitable for consensus algorithms. We finally conclude by presenting very recent studies about the performance of many of these control and estimation problems, which give rise to novel metrics for the consensus algorithms. These indexes of performance are rather different from more traditional metrics like the rate of convergence and have fundamental consequences on the design of consensus algorithms.