Šiame darbe nagrinėjami fraktalų – iteruoųjų funkcijų sistemų (IFS) atraktorių – sintezės algoritmai. Pagrindinis dėmesys skiriamas pabėgimo laiko (PL)-algoritmui. PL-algoritmas yra pakankamai universalus. Pagrindinės šio algoritmo panaudojimo sričitys – netiesinių dinaminių sistemų, veikiančių kompleksinėje plokštumoje, analizė, kompleksinių daugianarių šaknų pritraukimo baseinų vizualizavimas ir kt. Geometrinių fraktalų (IFS atraktorių) sintezei šis algoritmas iki šiol nebuvo naudojamas, nors tokia galimybė, kaip teorinis rezultatas, yra žinoma. Pagrindinė to priežastis – IFS sudarančių afiniųjų transformacijų veikimo zonų atskyrimo kriterijaus nebuvimas. Tokio kriterijaus paieškai ir realizacijai darbe skiriamas didžiausias dėmesys. Rezultatas – nauja adaptyvi IFS sudarančių afiniųjų transformacijų veikimo zonų atskyrimo procedūra. Lygegrečiai spendžiama tolygaus spalvinio sintezuojamo (PL-algoritmo pagalba) fraktalinio vaizdo užpildymo problema. Pasiūlytas originalus sprendimas – problemiškai oriantuota iteracij�� skaičiaus (sintezės metu) korekcija. Darbe pristatomi ir preliminarūs su fraktalinių vaizdų (IFS atraktorių) sinteze susijusių eksperimentų rezultatai. / The contribution of this work is a new version of the escape time algoritm adapted for synthesizing fractal images, indentified with atractors of iterated functions systems (IFS). The proposesd synthesis algorithm is based on the use of shift dynamics, associated with one or another IFS. The strategy for the seperation of extended domains of the inverse affine transformations, specified by IFS, is developed. In the field of computerized real word image models (digital images) the fractal approach is of outmost importance, because it facilitates perception and understanding of the information content of an image. To say more, it provides us with a powerful means to catch sight of a fundamental real word image property generally known as self-similarity. Due to this property, the research and development of algorithms („fractal techniques“) to extract imortant fractal parameters from appropriate digital data has received significant attention in recent years. In this work, the basic concepts and ideas that are needed to describe, state and solve the problem of synthesizing fractal images, identified with attractors of IFS, are introduced and explored. A new original approach (idea), leading to practical implementation of the shift dynamical system, associated with a particular IFS, is proposed (part 3). Some experimental results are given (Part 4).

As the greenhouse effect is an imminent concern, motivation for the development of energy efficient systems has grown fast. Today heavy-duty vehicles (HDVs) account for a growing part of the emissions from the vehicular transport sector. One way to reduce those emissions is by driving at short intervehicular distances in so called platoons, mainly on highways. In such formations, the aerodynamic drag is decreased which allows for more fuel efficient driving, meanwhile the roads are used more efficiently. This thesis deals with the question of how those platoons can be controlled without using communications between the involved HDVs. In this thesis, artificial neural networks are designed and trained to predict the velocity profile for an HDV driving over a section of road where data on the topography are available. This information is used in a model predictive controller to control the HDV driving behind the truck for which the aforementioned prediction is made. By having accurate information about the upcoming behaviour of the preceding HDV, the controller can plan the velocity profile for the controlled HDV in a way which minimizes fuel consumption. To ensure fuel optimal performance, a state describing the mass of consumed fuel is derived and minimized in the controller. A system modelling gear shift dynamics is proposed to capture essential dynamics such as torque loss during shifting. The designed controller is able to predict and change between the three highest gears making it able to handle almost all highway platooning scenarios. The prediction system shows great potential and is able to predict the velocity profile for different HDVs with an average error as low as 0.04 km/h. The controller is implemented in a simulation environment and results show that compared to a platoon without these predictions of the preceding HDV, the fuel consumption for the controlled HDV can be reduced by up to 6 %.