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master's thesis
Aproksimacija linearnih dinamičkih sistema u prostoru Hp×m2(C+)
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:336429
Mlinarić, Petar
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Mlinarić, P. (2014). Aproksimacija linearnih dinamičkih sistema u prostoru Hp×m2(C+) (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:336429

Mlinarić, Petar. "Aproksimacija linearnih dinamičkih sistema u prostoru Hp×m2(C+)." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:336429

Mlinarić, Petar. "Aproksimacija linearnih dinamičkih sistema u prostoru Hp×m2(C+)." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:336429

Mlinarić, P. (2014). 'Aproksimacija linearnih dinamičkih sistema u prostoru Hp×m2(C+)', Master's thesis, University of Zagreb, Faculty of Science, accessed 28 March 2025, https://urn.nsk.hr/urn:nbn:hr:217:336429

Mlinarić P. Aproksimacija linearnih dinamičkih sistema u prostoru Hp×m2(C+) [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2025 March 28] Available at: https://urn.nsk.hr/urn:nbn:hr:217:336429

P. Mlinarić, "Aproksimacija linearnih dinamičkih sistema u prostoru Hp×m2(C+)", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:336429

Metadata
TitleAproksimacija linearnih dinamičkih sistema u prostoru Hp×m2(C+)
AuthorPetar Mlinarić
MentorZlatko Drmač (mentor)
Committee memberZlatko Drmač (predsjednik povjerenstva)
Committee memberNela Bosner (član povjerenstva)
Committee memberVjeran Hari (član povjerenstva)
Committee memberFranka Miriam Bruckler (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-07-14, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Dinamički sistemi su svuda oko nas, od raznih prirodnih do industrijskih procesa. Za te procese se razvijaju modeli, koji se onda koriste za simuliranje ponašanja procesa i/ili za upravljanje nad njima. U svrhu povećanja preciznosti, javljaju se sve kompliciraniji modeli s kojima nije moguće efektivno računati. Stoga je potrebno tražiti reducirane modele, modele koji su jednostavniji, a dovoljno bliski kompliciranim modelima. U radu se promatraju linearni, vremensko-invarijantni,... More neprekidno-vremenski, konačnodimenzionalni, realni, stabilni sistemi oblika Ex′(t)=Ax(t)+Bu(t),y(t)=Cx(t), gdje su E,A∈Rn×n,B∈Rn×m i C∈Rp×n konstantne matrice, a x(t)∈Rn,u(t)∈Rmiy(t)∈Rp su stanje, ulaz i izlaz sistema. Za ovaj sistem se kaže da je n-dimenzionalan. Cilj redukcije modela je, za zadani n-dimenzionalni sistem, pronaći r-dimenzionalni sistem (gdje je r≪n takoder zadan), a da izlaz reduciranog modela bude što bliži izlazu punog modela. Smisao bliskosti modela koji se promatraju u radu je onaj dan normom Hardyjevog prostora Hp×m2(C+). U radu je obrađena metoda koja traži reducirani model koji zadovoljava neke nužne uvjete optimalnosti u H2 normi, dane u obliku tangencijalne Hermiteove interpolacije. Također je obrađena i metoda bazirana na Loewnerovim matricama koja ne ovisi realizaciji (E,A,B,C) i primjenjiva je za beskonačnodimenzionalne sisteme. Sve metode su testirane na primjerima iz Oberwolfach i NICONET baza te su rezultati uspoređeni s rezultatima dobivenim metodom balansiranog rezanja. Less
Abstract (english)
Dynamical systems are all around us, from various natural to industrial processes. Models are developed for these processes, which are then used to simulate the behavior of processes and/or to control over them. In order to increase the precision, there are more complicated models which can’t be effectively used. It is therefore necessary to look for reduced models, models that are simpler, but close enough to complicated models. Linear, time-invariant, continuous-time, finite... More dimensional, real, stable systems of the form Ex′(t)=Ax(t)+Bu(t),y(t)=Cx(t), are observed, where E,A∈Rn×n,B∈Rn×m and C∈Rp×n are constant matrices, and x(t)∈Rn,u(t)∈Rm and y(t)∈Rp are the state, input and output of the system. This system is said to be n-dimensional. The goal of model reduction is, for given n-dimensional system, to find an r-dimensional system (where r≪n is also given), such that the output of the reduced model is as close as possible to the output of the full model. The meaning of closeness which is used in this work is that which is given by the norm in the Hardy’s space Hp×m2(C+). This work presents a method that finds a reduced model satisfying some necessary conditions of optimality in H2 norm, given in the form of tangential Hermite interpolation. It also presents a method based on Loewner’s matrices which does not depend on any realization (E,A,B,C) and is applicable to infinite dimensional systems. All methods have been tested on examples from Oberwolfach and NICONET databases and the results are compared with the results obtained using balanced truncation. Less
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:336429
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-01-25 12:06:51
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