Cette thèse aborde le problème de l'analyse de la stabilité et de la conception des lois de commande pour les systèmes non linéaires mis sous la forme de modèles flous continus de type Takagi-Sugeno. L'analyse de stabilité est généralement basée sur la méthode directe de Lyapunov. Plusieurs approches existent dans la littérature, basées sur des fonctions de Lyapunov quadratiques sont proposées pour résoudre ce problème, les résultats obtenus à l'aide des telles fonctions introduisent un conservatisme qui peut être très préjudiciable. Pour surmonter ce problème, différentes approches basées sur des fonctions de Lyapunov non quadratiques ont été proposées, néanmoins ces approches sont basées sur desconditions très restrictives. L'idée développée dans ce travail est d'utiliser des fonctions de Lyapunov non quadratiques et des contrôleurs non-PDC afin d'en tirer des conditions de stabilité et de stabilisation moins conservatives. Les propositions principales sont : l'utilisation des bornes locales des dérivées partielles au lieu des dérivés des fonctions d’appartenances, le découplage du gain du régulateur des variables de décision de la fonction Lyapunov, l’utilisation des fonctions de Lyapunov floues polynomiales dans l’environnement des polynômes et la proposition de la synthèse de contrôleur vérifiant certaines limites de dérivés respectées dans une région de la modélisation à la place de les vérifier a posteriori. Ces nouvelles approches permettent de proposer des conditions locales afin de stabiliser les modèles flous continus de type T-S, y compris ceux qui n'admettent pas une stabilisation quadratique et obtenir des domaines de stabilité plus grand. Plusieurs exemples de simulation sont choisis afin de vérifier les résultats présentésdans cette thèse. / This thesis deals with the problem of stability analysis and control design for nonlinear systems in the form of continuous-time Takagi-Sugeno models. The approach to stability analysis is usually based on the direct Lyapunov method. Several approaches in the literature, based on quadratic Lyapunov functions, are proposed to solve this problem ; the results obtained using such functions introduce a conservatism that can be very detrimental. To overcome this problem, various approaches based on non-quadratic Lyapunov functions have also been recently presented; however, these approaches are based on very conservative bounds or too restrictive conditions. The idea developed in this work is to use non-quadratic Lyapunov functions and non-PDC controller in order to derive less conservative stability and stabilization conditions. The main proposals are : using local bounds in partial derivatives instead of time derivatives of the memberships,decoupling the controller gain from the Lyapunov function decision variables, using fuzzy Lyapunov functions in polynomial settings and proposing the synthesis of controller ensuring a priori known time-derivative bounds are fulfilled in a modelling region instead of checking them a posteriori. These new approaches allow proposing local conditions to stabilize continuous T-S fuzzy systems including those that do not admit a quadratic stabilization. Several simulation examples are chosen to verify the results given in this dissertation.

Spectrum, environment and location awareness are key characteristics of cognitive radio (CR). Knowledge of a user’s location as well as the surrounding environment type may enhance various CR tasks, such as spectrum sensing, dynamic channel allocation and interference management. This dissertation deals with the optimisation of adaptive localisation techniques for CR. The first part entails the development and evaluation of an efficient bandwidth determination (BD) model, which is a key component of the cognitive positioning system. This bandwidth efficiency is achieved using the Cramer-Rao lower bound derivations for a single-input-multiple-output (SIMO) antenna scheme. The performances of the single-input-single-output (SISO) and SIMO BD models are compared using three different generalised environmental models, viz. rural, urban and suburban areas. In the case of all three scenarios, the results reveal a marked improvement in the bandwidth efficiency for a SIMO antenna positioning scheme, especially for the 1×3 urban case, where a 62% root mean square error (RMSE) improvement over the SISO system is observed. The second part of the dissertation involves the presentation of a multiband time-of arrival (TOA) positioning technique for CR. The RMSE positional accuracy is evaluated using a fixed and dynamic bandwidth availability model. In the case of the fixed bandwidth availability model, the multiband TOA positioning model is initially evaluated using the two-step maximum-likelihood (TSML) location estimation algorithm for a scenario where line-of-sight represents the dominant signal path. Thereafter, a more realistic dynamic bandwidth availability model has been proposed, which is based on data obtained from an ultra-high frequency spectrum occupancy measurement campaign. The RMSE performance is then verified using the non-linear least squares, linear least squares and TSML location estimation techniques, using five different bandwidths. The proposed multiband positioning model performs well in poor signal-to-noise ratio conditions (-10 dB to 0 dB) when compared to a single band TOA system. These results indicate the advantage of opportunistic TOA location estimation in a CR environment. / Dissertation (MEng)--University of Pretoria, 2012. / Electrical, Electronic and Computer Engineering / unrestricted

In this paper we deal with the `strength' of ill-posedness for ill-posed linear operator equations Ax = y in Hilbert spaces, where we distinguish according_to_M. Z. Nashed [15] the ill-posedness of type I if A is not compact, but we have R(A) 6= R(A) for the range R(A) of A; and the ill-posedness of type II for compact operators A: From our considerations it seems to follow that the problems with noncompact operators A are not in general `less' ill-posed than the problems with compact operators. We motivate this statement by comparing the approximation and stability behaviour of discrete least-squares solutions and the growth rate of Galerkin matrices in both cases. Ill-posedness measures for compact operators A as discussed in [10] are derived from the decay rate of the nonincreasing sequence of singular values of A. Since singular values do not exist for noncompact operators A; we introduce stability rates in order to have a common measure for the compact and noncompact cases. Properties of these rates are illustrated by means of convolution equations in the compact case and by means of equations with multiplication operators in the noncompact case. Moreover using increasing rearrangements of the multiplier functions specific measures of ill-posedness called ill-posedness rates are considered for the multiplication operators. In this context, the character of sufficient conditions providing convergence rates of Tikhonov regularization are compared for compact operators and multiplication operators.

This paper deals with optimisation of food overloading at long distance flights. It is described how in case of two offered meals and two several passenger groups reserve meals are to distribute to both meals such that the probability that each passenger will get the meal of its choice is maximised. A statistical procedure is presented for estimation of needed demand probabilities.

The detection of multiple outliers can be interpreted as a model selection problem. Models that can be selected are the null model, which indicates an outlier free set of observations, or a class of alternative models, which contain a set of additional bias parameters. A common way to select the right model is by using a statistical hypothesis test. In geodesy data snooping is most popular. Another approach arises from information theory. Here, the Akaike information criterion (AIC) is used to select an appropriate model for a given set of observations. The AIC is based on the Kullback-Leibler divergence, which describes the discrepancy between the model candidates. Both approaches are discussed and applied to test problems: the fitting of a straight line and a geodetic network. Some relationships between data snooping and information criteria are discussed. When compared, it turns out that the information criteria approach is more simple and elegant. Along with AIC there are many alternative information criteria for selecting different outliers, and it is not clear which one is optimal.

Empirischen Studien zufolge können Patente sich positiv auf den Unternehmenserfolg auswirken. Allerdings wirkt dieser Effekt nicht automatisch, sondern Unternehmen müssen sich um den Aufbau und die gesteuerte Weiterentwicklung eines nachhaltigen und wertvollen Patentportfolios bemühen. Bisher ist jedoch nicht wissenschaftlich untersucht worden, welche Maßnahmen Unternehmen ergreifen können, um die unternehmensinternen Vorraussetzungen für eine erfolgreiche Steuerung von Patentaktivitäten zu schaffen. Um diese betrieblichen Faktoren zu identifizieren und deren Relevanz zu quantifizieren, wurden 2005 in einer breiten empirischen Untersuchung die aktiven Patentanmelder im deutschsprachigen Raum (über 1.000 Unternehmen) mit Hilfe eines standardisierten Fragebogens befragt. Auf der Basis von 325 auswertbaren Fragebögen (Ausschöpfungsquote 36,8 %) konnten zum einen Ergebnisse zum aktuellen Aufgabenspektrum der Patentabteilungen sowie zu deren organisatorischen und personellen Strukturen gewonnen werden. Ebenfalls wurde in dieser Status quo-Analyse der Bekanntheits- und Implementierungsgrad von Methoden und Systemen (z. B. Patentbewertungsmethoden, Patent-IT-Systeme) beleuchtet. Zum anderen wurden die betrieblichen Faktoren herausgestellt, auf die technologieorientierte Unternehmen achten sollten, um das Fundament für eine erfolgreiche Patentsteuerung zu legen. / Empirical studies have shown that patents can have a positive effect on corporate success. However, this effect does not occur by itself. Companies have to make an effort to create and to develop a sustainable patent portfolio. So far, no academic studies have investigated into which actions a company can take to establish the internal conditions for successful patent management. To identify and to quantify the relevance of these internal factors, a study was conducted using a standardized written questionnaire with more than 1,000 patent-oriented companies in the German-speaking countries (Germany, Austria, Switzerland, Liechtenstein). In total, 325 valid questionnaires were included in the analyses; this corresponds to an above-average response rate of 36.8 %. These analyses revealed insights into the current task profile of patent departments and their organizational and personnel structures. This status quo analysis also included the investigation into the awareness and implementation level of used methods and systems (e. g. patent evaluation methods, patent IT systems). Furthermore, the study could expose the internal determinants, which technology-oriented companies should focus on to ensure a successful patent management.

Black and Scholes have proposed a model for pricing European options where the underlying asset follows a so-called geometric Brownian motion which assumes constant volatility. The proposed Black-Scholes model has an exact solution. However, it has been shown that such an assumption of constant volatility is not realistic, and numerous extensions have been developed. In addition, models usually do not have a closed-form solution which makes pricing a challenging task. The thesis focuses on pricing Bermudan options under two stochastic volatility Heston-type models using an Almost-Exact scheme for simulation. Namely, we focus on deriving the Almost-Exact scheme for Heston and Double Heston model and numerically study the behaviour of the scheme. We show that the AES works well when the number of simulated steps is equal to the number of exercise dates which makes it efficient.

This study has been performed at Powertrain Engineering Sweden AB (PES), a fully owned subsidiary of Volvo Cars Group, which is constantly working to develop and improve internal combustion engines. As part of this work, durability tests are performed to analyse the impact of wear on the engines. At present, there is a strong focus on visual inspections after the engines have undergone durability tests. PES wants to develop a method where collected data from these tests can be used to explain how the phenomenon of knocking and the control of lambda changes over time. The study analyses one specific durability test and investigates the methodology of data analysis by using the open-source software platform Sympathy for Data, with an add-on developed by Volvo Cars Group, for data management, visualisation and analysis. To execute the analysis, engine parameters that affect these systems as well as parameters suitable to use as response variables are identified through literature studies of internal combustion engine fundamentalsas well as internal material, and knowledge acquired at the company. The result is presented in the form of an analysis generated by the node for partial least squares regression (PLSR) which is pre-programmed in Sympathy for Data as well as the images and graphs obtained as output. For knock, the signal for the final ignition angle was found to be suitable to use as the response variable in the PLSR. A suitable response variable for lambda was more difficult to identify, this is why both signals for the measured lambda and lambda adaptation are analysed. Studies of the internal material and knowledge highlighted the fact that several engine subsystems are highly dependent on each other and that even deeper research would be necessary to fully understand the process and identify the primary cause for the variations observed in the generated models. However, partial least squares regression was performed using parameters derived from literature reviews as input (predictors) in order produce regression models to explain the variance in sought response. Well-fitting models could be created with a varying number of latent variables needed for the different responses. The output obtained from the PLSR enables further studies of the specific cases as well as the methodology itself, hence, increase the use of data analysis with the help of the software used in the department for durability testing at PES. / Denna studie är utförd hos Powertrain Engineering Sweden AB (PES), vilka är ett helägt dotterbolag till Volvo Cars Group, som arbetar med att ta fram och förbättra förbränningsmotorer. En del i detta arbete är att genomföra långtidstest för att analysera hur motorernas egenskaper ändras vid förslitning över tid. I nuläget ligger stort fokus på visuella inspektioner efter att motorerna genomgått långtidstester. PES önskar utveckla en metod där redan insamlad data som registrerats i dessa tester kan förklara hur fenomenet knack och regleringen för lambda förändras över tid. Studien är genomförd i form av en fallstudie av ett specifikt långtidstest där den öppna programvaran Sympathy for Data, tillsammans med det av Volvo Cars Group utvecklade tillägget, används för datahantering, visualisering och analys. Studien undersöker också metodiken för dataanalys med nämnd programvara. För att genomföra detta identifieras motorparametrar som påverkar de undersökta systemen samt parametrar som lämpar sig att användas som responsvariabler i en regressionsmodell. Dessa parametrar togs fram genom litteraturstudier om de fundamentala delarna i en förbränningsmotor samt från företaget förvärvad intern kunskap kring systemen. Resultatet presenteras i form av en analys genomförd med den, i Sympathy for Data, förprogrammerade noden för partial least squares regression(PLSR) samt de bilder och grafer som erhålls. För knack visade det sig att den slutliga tändningsvinkeln var lämplig att använda som respons i PLSR-modellen. En lämplig responsvariabel för lambda var mer svåridentifierad, detta förklarar varför signalerna för uppmätt lambda och lambda adaption analyseras. Inläsning av internt material och grundläggande information om förbränningsmotorer visade att delsystem i ottomotorn är beroende och påverkas av varandra vilket innebär att mer ingående studier i dessa delsystem är nödvändigt för att förstå hela processen och hitta grundorsakerna till variationerna som påvisas för responssignalerna. Vidare utfördes PLSR med de parametrar som härletts från litteraturstudier som indatasignaler (prediktorer) för att skapa en regressionsmodell som förklarar variansen i sökta responssignaler. Beroende av responssignal krävdes varierande antal latenta variabler för att uppnå en tillräckligt precis modell. Resultatet från PLSR möjliggör vidare forskning inom området och metoden som använts och har på så sätt möjliggjort för fortsatt utveckling. Detta i sin tur kan öka användandet av dataanalys med hjälp av den programvara som används vid avdelningen för långtidstest hos PES.

In this thesis I apply modern econometric techniques on macroeconomic time series. Forecasting is here developed along several dimensions in the three chapters. The chapters are in principle self-contained. However, a common element is represented by the business cycle analysis. In the first paper, which primarily deals with the problem of forecasting euro area inflation in the short and medium run, we also compute the country-specific responses of a common business cycle shock. Both chapters 2 and 3 deal predominately with business cycle issues from two different perspectives. The former chapter analyses the business cycle as a dichotomous non-observable variable and addresses the issue of evaluating the euro area business cycle dating formulated by the CEPR committee, while the latter chapter studies the entire distribution of GDP growth. / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished

Tato práce se zaměřuje na datové struktury pro reprezentaci řídkých blokových matic a s nimi spojených výpočetních algoritmů, jež jsem navrhl. Řídké blokové matice se vyskytují při řešení mnoha dílčích problémů jako například při řešení metody nejmenších čtverců. Nelineární metoda nejmenších čtverců (NLS) je často aplikována v robotice pro řešení problému lokalizace robota (SLAM) nebo v příbuzných úlohách 3D rekonstrukce v počítačovém vidění (BA), (SfM). Problémy konečných elementů (FEM) a parciálních diferenciálních rovnic (PDE) v oboru fyzikálních simulací můžou také mít blokovou strukturu. Většina existujících implementací řídké lineární algebry používají řídké matice s granularitou jednotlivých elementů a jen několik málo podporuje řídké blokové matice. To může být způsobeno složitostí blokových formátů, jež snižuje rychlost výpočtů, pokud bloky nejsou dost velké. Některé ze specializovaných NLS optimalizátorů v robotice a počítačovém vidění používají blokové matice jako interní reprezentaci, aby snížily cenu sestavování řídkých matic, ale nakonec tuto reprezentaci převedou na elementovou řídkou matici pro implementaci k řešení systémů rovnic. Existující implementace pro řídké blokové matice se většinou soustředí na jedinou operaci, často násobení matice vektorem. Řešení navržené v této disertaci pokrývá širší spektrum funkcí: implementovány jsou funkce pro efektivní sestavení řídké blokové matice, násobení matice vektorem nebo jinou maticí a nechybí ani řešení trojúhelníkových systémů nebo Choleského faktorizace. Tyto funkce mohou být snadno použity ke řešení systémů lineárních rovnic pomocí analytických nebo iterativních metod nebo k výpočtu vlastních čísel. Jsou zde popsány rychlé algoritmy pro hlavní procesor (CPU) i pro grafické akcelerátory (GPU). Navrhované algoritmy jsou integrovány v knihovně SLAM++ , jež řeší problém nelineárních nejmenších čtverců se zaměřením na problémy v robotice a počítačovém vidění. Je provedeno vyhodnocení na standardních datasetech kde navrhované metody dosahují výrazně lepších výsledků než dosavadní metody popsané v literatuře -- a to bez kompromisů v přesnosti či obecnosti řešení.