ABSTRACT

The objective of this talk is twofold. In a first part of the talk, the classical notion of consensus for a multi-agent system will be reviewed. In the second part, a new approach for the estimation of network parameters of interest based on consensus algorithms will be presented.

The problem of consensus, i.e., driving the state of systems interacting in a network to a common value, has many interesting applications and has recently received much attention within the control community. Consensus is reached through a local interaction rule between the interconnected systems that can take many forms. Two main interactions rules are discussed: the first is the standard synchronous consensus rule, where all agents update their state at the same time: the second is an asynchronous consensus rules called gossip.

The emerging behavior of a multi-agent system is strictly related to the topology of the underlying network, which in turn is related to the spectrum of the Laplacian matrix of the network graph. In the last part of the talk a decentralized algorithm to estimate the Laplacian eigenvalues is presented. The basic idea is to provide a local interaction rule among agents so that their state trajectory is a linear combination of sinusoids oscillating only at frequencies function of the eigenvalues of the Laplacian matrix. In this way, the problem of decentralized estimation of the eigenvalues is mapped into a standard signal processing problem in which the unknowns are the finite number of frequencies at which the signal oscillates.