Esta tese apresenta novos algoritmos que resolvem problemas de estimativas filtrada, suavizadora e preditora para sistemas singulares no tempo discreto usando apenas argumentos determinísticos. Cada capítulo aborda inicialmente as estimativas para o sistema nominal e em seguida, as versões robustas para o sistema com incertezas limitadas. Os resultados encontrados podem ser aplicados tanto em sistemas invariantes como variantes no tempo discreto, utilizando a mesma estrutura do filtro de Kalman. Nos últimos anos, uma quantidade significativa de trabalhos envolvendo estimativas singulares foi publicada enfocando apenas a estimativa filtrada sob a justificativa de que a estimativa preditora era de significativa complexidade quando modelada pelo método dos mínimos quadrados. Por este motivo, poucos trabalhos, como NIKOUKHAH et al. (1992) e ZHANG et al. (1998), deduziram a estimativa preditora. Este último artigo apresentou também um algoritmo para a estimativa suavizadora, mas usando o modelo de inovação ARMA. No entanto, até onde foi possível identificar, nenhum trabalho até agora resolveu o problema de estimativa robusta, considerando incertezas nos parâmetros, para sistemas singulares. Para a dedução das estimativas singulares robustas, esta tese tomou como base SAYED (2001), que deduz o filtro de Kalman robusto com incertezas limitadas utilizando uma abordagem determinística, o chamado filtro BDU. Os filtros robustos para sistemas singulares apresentados nesta tese, são mais abrangentes que os apresentados em SAYED (2001). Quando particularizados para o espaço de estados sem incertezas, todos os filtros se assemelham ao filtro de Kalman. / New algorithms to optimal recursive filtering, smoothed and prediction for general time-invariant or time-variant descriptor systems are proposed in this thesis. The estimation problem is addressed as an optimal deterministic trajectory fitting. This problem is solved using exclusively deterministic arguments for systems with or without uncertainties. Kalman type recursive algorithms for robust filtered, predicted and smoothed estimations are derived. In the last years, many papers have paid attention to the estimation problems of linear singular systems. Unfortunately, all those works were concentrated only on the study of filtering problems, for nominal systems. The predicted and smoothed filters are more involved and were considered only by few works : NIKOUKHAH et al. (1992) and ZHANG et al. (1998) had proposed a unified approach for filtering, prediction and smoothing problems which were derived by using the projection formula and were calculated based on the ARMA innovation model, but they had not considered the uncertainties. In this thesis its applied for descriptor systems a robust procedure for usual state space systems developed by SAYED (2001), called BDU filter. It is obtained a robust descriptor Kalman type recursions for filtered, predicted and smoothed estimates. Considering the nominal state space, all descriptor filters developed in this work collapse to the Kalman filter.

L’objectif de cette thèse était de développer une méthode de synthèse de commande par retour d’état puis par observateurs offrant des conditions de synthèse non contraignantes dans le cas de systèmes non linéaires à temps discret. Dans cette méthode, est mise en exergue l’importance du choix de la description des systèmes sur l’étendue des résultats pouvant être obtenus lorsque la méthode d’étude de la stabilité est fixée. Ainsi l’utilisation des normes vectorielles comme fonction d’agrégation et du critère pratique de Borne et Gentina pour l’étude de la stabilité, associée à la description des systèmes par des matrices caractéristiques de forme en flèche de Benrejeb, a conduit à l’élaboration de nouvelles conditions suffisantes de stabilisation de systèmes dynamiques discrets non linéaires, formulées en théorèmes et corollaires. Ces résultats obtenus, sont ensuite exploités, avec succès, pour la formulation de nouvelles conditions suffisantes de vérification des propriétés de synchronisation pour les systèmes hyperchaotiques à temps discrets. Ensuite, le cas de synthèse d’observateur est validé dans deux types de transmission chaotique / The objective of this thesis was to develop a method for synthesizing control state feedback and observers by offering soft synthesis conditions in the case of nonlinear discrete-time systems. In this method, is highlighting the importance of choosing the systems description of the scope of what can be achieved when the stability study method is fixed. The use of of vector norms as an aggregation function and the practical Borne-Gentina criterion for stability study, associated to arrow form matrix of Benrejeb for system discription, lead to the development of new sufficient conditions for stabilization of nonlinear discrete dynamical systems, formulated as theorems and corollaries. These results are then used, with success, for the formulation of new sufficient conditions for checking properties of hyperchaotiques synchronization for discrete-time systems. Then, the synthesis of observer is validated in two types of chaotic transmission

This thesis studies the mixed data types kernel estimation framework for the models of discrete dependent variables, which are known as kernel discrete conditional functions. The conventional parametric multinomial logit MNL model is compared with the mixed data types kernel conditional density estimator in Chapter (2). A new kernel estimator for discrete time single state hazard models is developed in Chapter (3), and named as the discrete time “external kernel hazard” estimator. The discrete time (mixed) proportional hazard estimators are then compared with the discrete time external kernel hazard estimator empirically in Chapter (4). The work in Chapter (2) attempts to estimate a labour force participation decision model using a cross-section data from the UK labour force survey in 2007. The work in Chapter (4) estimates a hazard rate for job-vacancies in weeks, using data from Lancashire Careers Service (LCS) between the period from March 1988 to June 1992. The evidences from the vast literature regarding female labour force participation and the job-market random matching theory are used to examine the empirical results of the estimators. The parametric estimator are tighten by the restrictive assumption regarding the link function of the discrete dependent variable and the dummy variables of the discrete covariates. Adding interaction terms improves the performance of the parametric models but encounters other risks like generating multicollinearity problem, increasing the singularity of the data matrix and complicates the computation of the ML function. On the other hand, the mixed data types kernel estimation framework shows an outstanding performance compared with the conventional parametric estimation methods. The kernel functions that are used for the discrete variables, including the dependent variable, in the mixed data types estimation framework, have substantially improved the performance of the kernel estimators. The kernel framework uses very few assumptions about the functional form of the variables in the model, and relay on the right choice of the kernel functions in the estimator. The outcomes of the kernel conditional density shows that female education level and fertility have high impact on females propensity to work and be in the labour force. The kernel conditional density estimator captures more heterogeneity among the females in the sample than the MNL model due to the restrictive parametric assumptions in the later. The (mixed) proportional hazard framework, on the other hand, missed to capture the effect of the job-market tightness in the job-vacancies hazard rate and produce inconsistent results when the assumptions regarding the distribution of the unobserved heterogeneity are changed. The external kernel hazard estimator overcomes those problems and produce results that consistent with the job market random matching theory. The results in this thesis are useful for nonparametric estimation research in econometrics and in labour economics research.

The thesis write about the linear discrete time incremental estimators. These are used for the choice of the best control system in systems with variable structure and further for direct control with status controller. There is an application of this on physical plane. In this paper PID variation controllers are discussed and optimized using Nelder-Mead Simplex Method. Feedback control with optimal PID is compared with control using linear discrete incremental estimators and status regulator.

Robbins' problem is an optimal stopping problem where one seeks to minimize the expected rank of their observations among all observations. We examine random walk analogs to Robbins' problem in both discrete and continuous time. In discrete time, we consider full information and relative ranks versions of this problem. For three step walks, we give the optimal stopping rule and the expected rank for both versions. We also give asymptotic upper bounds for the expected rank in discrete time. Finally, we give upper and lower bounds for the expected rank in continuous time, and we show that the expected rank in the continuous time problem is at least as large as the normalized asymptotic expected rank in the full information discrete time version.

Indiana University-Purdue University Indianapolis (IUPUI) / In recent years, there have been a lot of technology innovations to automate the day to day processes done by every person. These days the automobile manufacturers introduce new features in their cars, in order to improve customer experience, like Adaptive cruise control, Parallel park assist, etc. The objective of this thesis is to model an automated parallel parking system and to simulate the system behavior, by taking into account the high level events which happen when a car is parallel parked. The tool used in this thesis to model and simulate the system is Hybrid Petri net (HPN), which is versatile to model the real life systems. Chapter 1 deals with a brief introduction of the related work in Hybrid Petri net modeling of real life systems, automatic parallel parking systems and how the concept for modeling the parallel parking system was developed. Chapter 2 deals with the general introduction about Discrete, Continuous and Hybrid Petri nets and their dynamics which are essential for understanding this thesis. Chapter 3 deals with the development of the model and the various stages in the model development. Errors encountered in each stage is briefly discussed and the improvements are discussed in the next stage of development. This chapter concludes with the final integrated model and operation of the model. Chapter 4 deals with the discussion of results obtained when the model is tested in MATLAB and SIMHPN (which is a Matlab embedded simulation program). The results are compared, the system behavior is observed and the purpose of the thesis is justified. In Chapter 5, a conclusion is provided to summarize the entire thesis.

We consider a single-product dynamic inventory problem where the demand distributions in each period are known and independent but with density. We assume the lead time and the fixed cost for ordering are zero and that there are no capacity constraints. There is a holding cost and a backorder cost for unfulfilled demand, which is backlogged until it is filled by another order. The problem may be nonstationary, and in fact our approximation of the optimal cost function using splines is most advantageous when demand falls suddenly. In this case the myopic policy, which is most often used in practice to calculate optimal inventory level, would be very costly. Our algorithm uses quadratic splines to approximate the optimal cost function for this dynamic inventory problem and calculates the optimal inventory level and optimal cost.

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本研究將財務危機分為『經營不善型財務危機』以及『掏空型財務危機』兩種類型，運用離散時間涉險方法，分析公司在不同財務狀況以及公司治理機制下，發生『經營不善型財務危機』的可能性。另外，本研究也探討『經營不善型財務危機』對公司獲利能力的敏感性，是否也受到公司治理的影響。 以民國85-94年上市櫃公司為研究對象，實證結果顯示當公司治理機制強，而財務狀況弱時，最有可能發生『經營不善而非掏空型』財務危機。再者，公司治理機制，會增強財務危機對財務狀況的敏感程度。 / This study classifies financial distress into two types: operating-failure financial distress and fraud financial distress. Based on business performance and corporate governance while employing discrete-time survival model, it analyzes the probability of the operating-failure financial distress. Furthermore, this study also examines if the sensitivity of operating-failure financial distress to profitability is moderated by corporate governance. Firms listed in Taiwan Stock Exchange during 1996-2005 are selected as sample. The empirical results indicate that firms with good corporate governance and bad business performance are most likely to encounter operating-failure financial distress. Furthermore, the corporate governance moderates the sensitivity of the operating-failure financial distress to profitability.