Browsing by Author "Wieland, Peter"

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    Communication networks in control: new dimensions of complexity
    (2009) Allgöwer, Frank; Blind, Rainer; Münz, Ulrich; Wieland, Peter
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    From static to dynamic couplings in consensus and synchronization among identical and non-identical systems
    (2010) Wieland, Peter; Allgöwer, Frank (Prof. Dr.-Ing.)
    In a systems theoretic context, the terms 'consensus' and 'synchronization' both describe the property that all individual systems in a group behave asymptotically identical, i.e., output or state trajectories asymptotically converge to a common trajectory. The objective of the present thesis is an improved understanding of some of the diverse coupling mechanisms leading to consensus and synchronization. A starting point is the observation that classical consensus and synchronization results commonly deal with two distinct facets of the problem: Consensus has regularly a strong focus on the interconnections and related constraints while the individual systems possess simple dynamics. Synchronization, in contrast, typically addresses questions about complex individual dynamical systems and puts weak emphasis on communication constraints. Very few results exist that address both facets simultaneously. A thorough analysis of static couplings in consensus algorithms provides explanations for this observation by unveiling limitations inherent to this type of couplings. Novel dynamic coupling mechanisms are proposed to overcome these limitations. These methods essentially rely on an internal model principle for consensus and synchronization derived in the thesis. This principle provides necessary conditions for consensus and synchronization in groups of non-identical systems, and it establishes a link to the output regulation problem. The fresh point of view revealed by this link eventually leads to a new hierarchical mechanism for consensus and synchronization, where coupling dynamics compensate for heterogeneity in the dynamical models of the individual systems as well as communication constraints. Applications include synchronization of linear systems and phase synchronization of exponentially stable oscillators.