We examine the related nature of two identification algorithms, subspace identification (SID) and Dynamic Mode Decomposition (DMD), and their correctness properties over a broad range of problems. This investigation begins by noting the strong relationship between the two algorithms, both drawing significantly on the pseudoinverse calculation using singular value decomposition, and ultimately revealing that DMD can be viewed as a substep of SID. We then perform extensive computational studies, characterizing the performance of SID on problems of various model orders and noise levels. Specifically, we generate 10,000 random systems for each model order and noise level, calculating the average identification error for each case, and then repeat the entire experiment to ensure the results are, in fact, consistent. The results both quantify the intrinsic algorithmic error at zero-noise, monotonically increasing with model complexity, as well as demonstrate an asymptotically linear degradation to noise intensity, at least for the range under study. Finally, we close by demonstrating DMD's ability to recover system matrices, because its access to full state measurements makes them identifiable. SID, on the other hand, can't possibly hope to recover the original system matrices, due to their fundamental unidentifiability from input-output data. This is true even when SID delivers excellent performance identifying a correct set of equivalent system matrices.

Time series data is very common in our daily life. Since they are related to time, most of them show a periodicity. The existence of this periodic in uence leads to our research problem, seasonal adjustment. Seasonal adjustment is generally applied around us, especially in areas of economy and nance. Over the last few decades, scholars around the world made a lot of contributions in this area, and one of the latest methods is X-13ARIMA-SEATS, which is built on ARIMA models and linear lters. On the other hand, state space modelling (abbreviated to SSM) is also a popular method to solve this problem and researchers including J. Durbin, S.J. Koopman and and A. Harvery have contributed a lot of work to it. Unlike linear lters and ARIMA models, the study on SSM starts relatively late, thus it has not been studied and developed widely for the seasonal adjustment problem. And SSMs have a lot advantages over those ARIMA-based and lter-based methods such as exibility, the understandable structure and the potential to do partial pooling, but in practice, its default decomposition result behaves bad in some cases, such as excessively spiky trend series; on the contrary, X-13ARIMA-SEATS could output good decomposition result for us to analyze, but it can't be tweaked or combined as easily as generative models and behaves like a black-box. In this paper, we shall use Bayesian inference to combine both methods' characteristics together. Simultaneously, to show the advantage of using SSMs concretely, we shall give a simple application in partial pooling and talk about how to apply the Bayesian analysis to partial pooling.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第20024号 / 情博第619号 / 新制||情||108(附属図書館) / 33120 / 京都大学大学院情報学研究科知能情報学専攻 / (主査)教授 松山 隆司, 教授 熊田 孝恒, 准教授 川嶋 宏彰 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Control theory can be used to make an unstable system stable. This thesis seeks to do this, where the system is a two DOF inverted pendulum with reaction wheels for stabilisation. The thesis also seeks to answer what is most important for making it stabilize for a longer period of time. It was decided that a state space controller was to be used with various sensors measuring the states. To be able to design a functioning demonstrator, a mathematical model of the system dynamics was developed. In the end the demonstrator proved to function as desired, being able to balance indefinitely. It was found that it is absolutely necessary to either give the controller a perfect set point or to implement an automatic set point. / Reglerteknik kan användas för att göra ostabila system stabila. Målet med detta projekt var att göra detta med ett system i form av en inverterad pendel med två frihetsgrader som balanseras med hjälp av två svänghjul. Projektet söker att besvara frågan om vad som är de viktigaste faktorerna för att få systemet att vara stabilt över en längre tid. En tillståndsåterkoppling användes som regulator vilket innebar att flera olika sensorer behövdes för att mäta de olika tillstånden. För att kunna konstruera en fungerande prototyp utvecklades en matematisk modell av systemet vilken användes för simulering av systemet. Till slut konstruerades en fungerade prototyp som till synes kunde balansera över oöverskådlig tid. En av de faktorer som visade sig påverka huruvida systemet uppnår stabilitet över längre tid var hur bra referenspunkt som gavs till regulatorn, det vill säga det tillstånd som regulatorn reglerar systemet mot. Det visade sig vara möjligt att implementera en självjusterande referenspunkt som gjorde systemet stabilt över tid.

[pt] Nesta Tese, eu me concentro em desenvolvimentos sobre o filtro de Kalman sujeito a restrições lineares gerais. Há essencialmente três tipos de contribuições: (i) provas alternativas para resultados previamente estabelecidos na literatura sobre o filtro de Kalman com restrições; (ii) resultados que presumidamente destacam aspectos teóricos e metodológicos para modelagens em espaço de estado sob restrições; e (iii) aplicações que parecem ser inéditas até então em finanças (análise de investimentos) e em macroeconomia, nas quais os métodos propostos são ilustrados e avaliados. No final, eu sugiro algumas extensões adicionais sobre o tema, as quais, novamente, dividem-se em teoria, métodos e aplicações. / [en] In this Thesis, I bring the attention to developments on Kalman filtering subject to general linear constraints. There are essentially three kinds of contributions: (i) new proofs for already established results within the restricted Kalman filtering literature; (ii) new results which are supposed to shed light on theoretical and methodological frameworks for linear state space modeling under linear restrictions; and (iii) applications that seem to be new in investment analysis and in macroeconomics, where the proposed methods are illustrated and evaluated. At the end, I suggest some further extensions in the subject, which, again, step into theory, methods and applications.

This dissertation explores how experience and environment impact behavior. In the first chapter, I provide behavioral foundations for a model of taste uncertainty with endogenous learning through consumption. In this setting, uncertainty is over an unobservable, subjective state space. Preference over lottery-menu pairs is sufficient to identify the state space and the learning process. In this model, the agent is viewed as if he learns the utility of an object upon its consumption. This information is used to improve choice from the follow-on menu. This implies a trade-off between consumption value and information leading to experimentation. I provide a behavioral definition of experimentation. While the literature focuses on identifying subjective states through a demand for flexibility, I show that experimentation also (partially) identifies taste uncertainty. The second chapter explores the potential for social networks to affect decisions of political leaders. To this end we construct a database linking European royal kinship networks, monarchies, and wars to study the effect of family ties on conflict. To establish causality, we exploit decreases in connection caused by apolitical deaths of network important individuals. These deaths are associated with substantial increases in the frequency and duration of war. We provide evidence that these deaths affect conflict only through changing the kinship network. Over our period of interest, the percentage of European monarchs with kinship ties increased threefold. Together, these findings help explain the well-documented decrease in European war frequency. The final chapter builds on the robust finding from the psychology literature that the co-presentation of products causes consumers to associate them. Associated products are evaluated more similarly. Supposing that agents behave according to this evidence, I axiomatically derive a tractable utility model of this association effect. In an application, I study a two-product monopolist that can strategically choose whether or not to offer his products under the same brand. I demonstrate that psychological association can provide strict incentives for either brand extension or brand differentiation depending on the distribution of product valuations in the market. Appropriate branding strategies allow firms to extract more surplus from consumers when psychological association is present.

Transverse ply cracking often leads to the loss of stiffness and reduction in thermal expansion coefficients. This paper presents the thermoelastic degradation of general cross-ply laminates, containing transverse ply cracks, subjected to biaxial extension, bending and thermal loading. The stress and displacement fields are calculated by using the state space equation method [Zhang D, Ye JQ, Sheng HY. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos Struct [in press].]. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. After introducing the concept of the effective thermoelastic properties of a laminate, the degradations of axial elastic moduli, Poisson¿s ratios, thermal expansion coefficients and flexural moduli are predicted and compared with numerical results from other methods or available test results. It is found that the theory provides good predictions of the stiffness degradation in both symmetric and antisymmetric cross-ply laminates. The predictions of stiffness reduction in nonsymmetric cross-ply laminates can be used as benchmark test for other methods.

Yes / A dynamic response analysis model of a Class E2 converter for wireless power transfer applications is presented. The converter operates at 200 kHz and consists of an induction link with its primary coil driven by a class E inverter and the secondary coil with a voltage-driven class E synchronous rectifier. A seventh-order linear time invariant state-space model is used to obtain the eigenvalues of the system for the four modes resulting from the operation of the converter switches. A participation factor for the four modes is used to find the actual operating point dominant poles for the system response. A dynamic analysis is carried out to investigate the effect of changing the separation distance between the two coils, based on converter performance and the changes required of some circuit parameters to achieve optimum efficiency and stability. The results show good performance in terms of efficiency (90–98%) and maintenance of constant output voltage with dynamic change of capacitance in the inverter. An experiment with coils of the dimension of 53 × 43 × 6 mm3 operating at a resonance frequency of 200 kHz, was created to verify the proposed mathematical model and both were found to be in excellent agreement.

Transverse ply cracking often leads to the loss of stiffness and reduction in thermal expansion coefficients. This paper presents the thermoelastic degradation of general cross-ply laminates, containing transverse ply cracks, subjected to biaxial extension, bending and thermal loading. The stress and displacement fields are calculated by using the state space equation method [Zhang D, Ye JQ, Sheng HY. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos Struct [in press].]. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. After introducing the concept of the effective thermoelastic properties of a laminate, the degradations of axial elastic moduli, Poisson's ratios, thermal expansion coefficients and flexural moduli are predicted and compared with numerical results from other methods or available test results. It is found that the theory provides good predictions of the stiffness degradation in both symmetric and antisymmetric cross-ply laminates. The predictions of stiffness reduction in nonsymmetric cross-ply laminates can be used as benchmark test for other methods.

Ever faster data transmission in wireless communication is desired to satisfy emerging markets for various media services, such as voice, picture and video calls, multimedia messaging, music and video downloads, and even television. With the explosive increase in the use of mobile devices such as cellular phones, PDAs, GPS, and laptop computers, power consumption has become a prime consideration in the design of mobile communication systems. In order to reliably maintain a high rate of transmission and low power consumption, it is imperative that the receiver obtains as much knowledge as possible about the current state of the channel. A more accurate model of wireless communication channels will indisputably help in obtaining more knowledge about the transient channel state, providing a more accurate and efficient reproduction of the transmitted signal, and decreased power consumption by the receiver. With careful choice and consideration of the channel model, systemic optimization based on the selected channel model will improve the system performance of the transmitter and receiver through better encoding and decoding, as well as through better control of transmitted signal's power level. This thesis focuses on understanding the physical and statistical characteristics of wireless channels, and investigates how to represent wireless channels using simple mathematical models. This thesis initially studied a simple time-varying stationary channel, i.e.a multipath fiat fading channel without terminal motion, which is typically used for indoor wireless communication. With an introduction of stochastic differential equations, we derived a first-order AR stochastic process to represent this stationary channel. For a general multipath fiat fading channel with terminal motion, the traditional Clarke's model was then extended by incorporating the effects of fluctuations in the component phases and analyzed statistically. The resulting theoretical power spectrum was shown to fit practical measured spectra, in contrast to the traditional theoretical fiat fading channel spectra (Jakes' spectrum in [19]) . Finally, we developed a state-space model that represents a wireless channel using these modified spectral characteristics. This was achieved by developing a relationship between the state-space model and the theory of a rational transfer function. A novel method for designing a rational transfer function for linear systems was then proposed. In this method, the rational transfer function is represented via the Observable Canonical Form (OCF) to obtain the state-space model, which can be used to represent and simulate a fiat fading wireless channel. The presented state-space approach is simple and provides rapid computation. The present AR and state-space models provide valuable contributions that can be integrated with other algorithms for better system optimization of wireless communication networks. / Thesis / Doctor of Philosophy (PhD)