<p>U doktorskoj disertaciji obrađen je problem upravljanja montažnim<br />sistemima pomoću bežične senzorske tehnologije u cilju poboljšanja<br />efikasnosti proizvodnje i poboljšanja kvaliteta proizvoda. U okviru<br />ove disertacije je razvijen model bežičnog upravljačkog sistema za<br />upravljanje i nadzor industrijskih procesa. Glavni cilj istraživanja<br />je razvoj integrisanog sistema za praćenje pozicije radnog predmeta i<br />praćenje okolnosti u kojima se radni predmet nalazi u montažnim<br />sistemima. Rezultati istraživanja su potvrđeni eksperimentalnim<br />istraživanjem u laboratorijskoj i u realnoj industrijskoj sredini.</p> / <p>The dissertation deals with the problem of monitoring and controlling<br />industrial assembly lines by wireless sensor technology with the aim of<br />improving the efficiency of production and the quality of the product. A model<br />of a wireless controlling system has been developed for monitoring and<br />controlling industrial processes. The main focus of the study is the<br />development of an integrated system for monitoring the position of the<br />product and the influences on the product in the assembly lines. The results<br />are confirmed by experiments in a laboratory and real industrial environment.</p>

The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean distance matrix and faces of the semidefinite cone containing the feasible set of the semidefinite relaxation. We show how using semidefinite facial reduction allows us to dramatically reduce the number of variables and constraints required to represent the semidefinite feasible set. We have used this theory to develop a highly efficient algorithm capable of solving many very large Euclidean distance matrix completion problems exactly, without the need for a semidefinite optimization solver. For problems with a low level of noise, our SNLSDPclique algorithm outperforms existing algorithms in terms of both CPU time and accuracy. Using only a laptop, problems of size up to 40,000 nodes can be solved in under a minute and problems with 100,000 nodes require only a few minutes to solve.

The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean distance matrix and faces of the semidefinite cone containing the feasible set of the semidefinite relaxation. We show how using semidefinite facial reduction allows us to dramatically reduce the number of variables and constraints required to represent the semidefinite feasible set. We have used this theory to develop a highly efficient algorithm capable of solving many very large Euclidean distance matrix completion problems exactly, without the need for a semidefinite optimization solver. For problems with a low level of noise, our SNLSDPclique algorithm outperforms existing algorithms in terms of both CPU time and accuracy. Using only a laptop, problems of size up to 40,000 nodes can be solved in under a minute and problems with 100,000 nodes require only a few minutes to solve.