New methods for consensus in multiagent systems

Abstract

Consensus refers to achieving an agreement on a variable of interest on all the agents in a multiagent system by sharing and/or acquiring information within other agents. Its applications are given in the field of multiagent systems that work cooperatively by sharing information in a networked manner. Many problems such as formation control,flocking, and platoon, can be addressed using consensus-based approaches. Additionally, as communication and processing rely on processes subject to time-delays, the analysis of the delays is of major importance for networked applications, as it may cause greatimpact in the systems response, avoiding or enabling consensus and consequently the execution of the task. The starting point of the methodology is the translation of the consensus problem into a stability problem, thus analyzed with the vast theory for linear systems. The impacts of delays in communication and input delays are presented toshow the importance of analyzing the delays in intervals considering lower and upper bounds for time-varying delays. Thereby, results considering the analysis of consensus with the considered bounds are presented by means of sufficient conditions described by linear matrix inequalities (LMIs), using Lyapunov-Krasovskii theory. Failures in thecommunication links, changes in the agents arrangement, or obstructions on sensing are described by switching topologies, modeled as Markov jump linear systems, with uncertain transition rates. In order to increase the delay margins or improve convergence rate of the system, a method for the design of the coupling strengths is presented, also by means of LMIs. Finally, single-order consensus is applied in real-world problems in cooperative robotics, based on the extension of consensus on dual quaternions, which describe the pose of rigid-bodies adequately. Through all the text, examples are presented to show the performance of the methods with application-oriented problems.