Energy-Aware Consensus For Networked Sampled MIMO Systems

Abstract

AbstractThis work presents a method to compute the optimal sampling time that makes N MIMO agents converge to the consensus state with minimum energy consumption. In its turn, every agent in the network is composed of n continuous time first order linear systems. The communication is done in discrete time, sampling all the signals associated to every agent at the same sampling time. In order to minimize the energy consumed in the process of communication, we will look for the optimal sampling time such that the consensus is reached in a minimum number of iterations. The analysis is performed by minimizing objective functions that take into account a measure of the convergence rate to reach a consensus. These objective functions mainly depend on the eigenvalues of the sampled transition matrix of the system. The method can be applied to medium/large scale networks, since it requires computing the eigenvalues of the adjacency matrix just once. Finally, we present a case study based on the torus topology, where a MIMO case of communication (1000 systems) is analyzed, obtaining the optimal sampling time to reach the consensus.