Adaptive Synchronization over Uncertain Multi-Agent Systems

Abstract

A challenging task in synchronization of multi-agent systems is steering the network towards a coherent solution when the dynamics of the constituent systems are heterogeneous and residing in a possibly large uncertainty set. In this situation, synchronization can be achieved via adaptive protocols (with adaptive feedback gains, or adaptive coupling gains, or both). However, as state-of-the-art synchronization methods adopt a distributed observer architecture, they require to communicate extra local observer variables among neighbors, in addition to the neighbors' states (or outputs). The distinguishing feature of this work is to show that synchronization in heterogeneous and uncertain multi-agent systems is possible without the need for any distributed observer. This can be achieved by designing adaptive distributed synchronization protocols, based on homogenization reasoning. Specifically, ideal gains are defined (feedback and coupling gains) that could lead all the heterogeneous agents to a desired homogeneous behavior and thus synchronization. However, since these gains are unknown in view of the unknown dynamics, we design adaptive laws for these gains that lead the agents toward synchronization. In this thesis, different control protocols are designed to address both leaderless and leader-follower synchronization of linear multi-agent systems. The protocols are then extended to achieve synchronization over a special class of nonlinear multi-agent systems, whose units are modeled as Kuramoto-like systems. Throughout this work, convergence of the synchronization error to zero is shown via Lyapunov analysis, and numerical examples demonstrate the effectiveness of the proposed protocols.