{"data":{"id":"10.13016/m2nd0p","type":"dois","attributes":{"doi":"10.13016/m2nd0p","prefix":"10.13016","suffix":"m2nd0p","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Somarakis, Christoforos","nameType":"Personal","givenName":"Christoforos","familyName":"Somarakis","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"PROBLEMS IN DISTRIBUTED CONTROL SYSTEMS, CONSENSUS AND FLOCKING NETWORKS"}],"publisher":"Digital Repository at the University of Maryland","container":{},"publicationYear":2015,"subjects":[{"subject":"Mathematics","subjectScheme":"pqcontrolled"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subjectScheme":"pquncontrolled"}],"contributors":[],"dates":[{"date":"2015","dateType":"Issued"}],"language":"en","types":{"ris":"THES","bibtex":"phdthesis","citeproc":"thesis","schemaOrg":"Thesis","resourceType":"Dissertation","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[],"descriptions":[{"description":"An important variant of the linear model is the delayed one where it is discussed\n\nin great detail under two theoretical frameworks: a variational stability analysis\n\nbased on fixed point theory arguments and a standard Lyapunov-based analysis.\n\nThe investigation revisits scalar variation unifying the behavior of old biologically\n\ninspired model and extends to the multi-dimensional (consensus) alternatives. We\n\ncompare the two methods and assess their applicability and the strength of the\n\nresults they provide whenever this is possible.\n\nThe obtained results are applied to a number of nonlinear consensus networks.\n\nThe first class of networks regards couplings of passive nature. The model is considered\n\non its delayed form and the linear theory is directly applied to provide strong\n\nconvergence results. The second class of networks is a generally nonlinear one and\n\nthe study is carried through under a number of different conditions. In additions the\n\nnon-linearity of the models in conjunction with delays, allows for new type of synchronized solutions. We prove the existence and uniqueness of non-trivial periodic\n\nsolutions and state sufficient conditions for its local stability. The chapter concludes\n\nwith a third class of nonlinear models. We introduce and study consensus networks\n\nof neutral type. We prove the existence and uniqueness of a consensus point and\n\nstate sufficient conditions for exponential convergence to it.\n\nThe discussion continues with the study of a second order flocking network of\n\nCucker-Smale or Motsch-Tadmor type. Based on the derived contraction rates in the\n\nlinear framework, sufficient conditions are established for these systems' solutions to\n\nexhibit exponentially fast asymptotic velocity. The network couplings are essentially\n\nstate-dependent and non-uniform and the model is studied in both the ordinary and the delayed version. The discussion in flocking models concludes with two noisy\n\nnetworks where convergence with probability one and in the r-th square mean is\n\nproved under certain smallness conditions. \n\nThe linear theory is, finally, applied on a classical problem in electrical power\n\nnetworks. This is the economic dispatch problem (EDP) and the tools of the linear\n\ntheory are used to solve the problem in a distributed manner. Motivated by the\n\nemerging field of Smart Grid systems and the distributed control methods that are\n\nneeded to be developed in order to t their architecture we introduce a distributed\n\noptimization algorithm that calculates the optimal point for a network of power\n\ngenerators that are needed to operate at, in order to serve a given load. In particular,\n\nthe power grid of interconnected generators and loads is to be served at an optimal\n\npoint based on the cost of power production for every single power machine. The\n\npower grid is supervised by a set of controllers that exchange information on a\n\ndifferent communication network that suffers from delays. We define a consensus\n\nbased dynamic algorithm under which the controllers dynamically learn the overall\n\nload of the network and adjust the power generator with respect to the optimal\n\noperational point.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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