From static to dynamic couplings in consensus and synchronization among identical and non-identical systems

Auteurs

• Peter Wieland

Paramètres

• Informatique, programmation

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In a systems theoretic context, 'consensus' and 'synchronization' describe how individual systems in a group behave identically over time, with their outputs or state trajectories converging to a common path. This thesis aims to enhance the understanding of various coupling mechanisms that lead to these phenomena. It begins by noting that traditional results often focus separately on consensus, which emphasizes interconnections and constraints, and synchronization, which deals with complex individual dynamical systems. Few studies address both aspects simultaneously. A detailed examination of static couplings in consensus algorithms reveals inherent limitations, prompting the introduction of novel dynamic coupling mechanisms designed to address these issues. These methods are based on an internal model principle for consensus and synchronization, offering necessary conditions for groups of non-identical systems and linking to the output regulation problem. This new perspective ultimately leads to a hierarchical mechanism for achieving consensus and synchronization among complex non-identical systems, requiring minimal assumptions about interconnections. Applications of these findings include synchronization of linear systems and phase synchronization of nonlinear oscillators.

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• Année de publication: 2010