This work is an extension of the classical Cox-Ross-Rubinstein discrete time market model in which only one risky asset is considered. We introduce another risky asset into the model. Moreover, the random structure of the asset price sequence is generated by bivariate finite state Markov chain. Then, the interest rate varies over time as it is the function of generating sequences. We discuss how the model can be adapted to the real data. Finally, we illustrate sample implementations to give a better idea about the use of the model.

This thesis investigates the frequency weighted balanced model reduction problem for linear time invariant systems. Both continuous and discrete time systems are considered, in one and two-dimensions. First the frequency weighted balanced model reduction problem is formulated, then a novel frequency weighted, balanced, model reduction method for continuous time systems is proposed. This method is based on the retention of frequency weighted Hankel singular values of the original system, and yields stable reduced order models even when two sided weightings are employed. An alternative frequency weighted balanced model reduction technique (applicable for controller reduction applications) is then developed. This is based on a parametrized combination of the frequency weighted partial fraction expansion technique with balanced truncation and the singular perturbation approximation techniques. This method yields stable models even when two sided weightings are employed. An a priori error bound for the model reduction method is derived. Lower frequency response errors and error bounds are obtained using free parameters and equivalent anti-stable weightings. Based on the same idea, a novel parameterized frequency weighted optimal Hankel norm model reduction method with a tighter a priori error bound is proposed. The proposed methods are extended to include discrete time systems. A frequency interval Gramians based stability preserving model reduction scheme with error bounds is also presented. In this case, frequency weights are not explicitly predefined. Discrete time system related results are also included. Several frequency weighted model reduction results for two-dimensional (2-D) systems are also proposed. The advantages of these schemes include error bounds, guaranteed stability and applicability to general stable (non-separable denominator) weighting functions. Finally, a novel 2-D identification based frequency weighted model reduction scheme is outlined. Numerically robust algorithms based on square root and balancing free techniques are proposed for frequency weighted balanced truncation techniques. Several practical examples are included to illustrate the effectiveness of the algorithms.

Este trabalho apresenta uma proposta de um software de simulação e diagnóstico de falhas aplicado a um sistema de automação. para realizar esta tarefa foi desenvolvido um estudo de caso que contem um problema de automação industrial. Deste estudo foi retirado um modelo, usado como base para criar do software de simulação que segue as especificações dos modelos, no qual é possível observar a evolução dos eventos através de sua linguagem e diagnosticar falhas, quando estas ocorrem em uma das máquinas da planta. O processo de diagnóstico de falhas tem como base as regras de diagnosticabilidade apresentadas na literatura. As máquinas, assim como suas restrições, são modeladas dentro do próprio software, onde são definidas as estruturas de cada automato assim como características como observabilidade, controlabilidade e a possibilidade de falhar. Os testes realizados no sistema apresentado mostraram que a linguagem de controle consegue, mesmo permitindo um nivel de liberdade ao sistema, identificar as falhas verificando somente para os eventos que ocorrem após a ocorrência da mesma. / This work we presents a proposal a software of simulation and fault diagnosis applied to an automation system. In that task was developed , a case study that contains a problem of industrial automation. The study was used as the source for creating the simulation that follows the specifications of software models, where you can observe the evolution of events through its language and diagnose faults when they occur in one of the machines of the plant. The process of fault diagnosis is based on the rules of diagnosticabilidades presented in the literature. The machines, as well as its restrictions are modeled within the software itself, where the structures of each automaton are defined the caracteristics as observability an the possibility of failure. The tests in the system showed that of the language used can allowing identify fails, checking only for events that occorem after the occurence the fails.

Este trabalho apresenta uma proposta de um software de simulação e diagnóstico de falhas aplicado a um sistema de automação. para realizar esta tarefa foi desenvolvido um estudo de caso que contem um problema de automação industrial. Deste estudo foi retirado um modelo, usado como base para criar do software de simulação que segue as especificações dos modelos, no qual é possível observar a evolução dos eventos através de sua linguagem e diagnosticar falhas, quando estas ocorrem em uma das máquinas da planta. O processo de diagnóstico de falhas tem como base as regras de diagnosticabilidade apresentadas na literatura. As máquinas, assim como suas restrições, são modeladas dentro do próprio software, onde são definidas as estruturas de cada automato assim como características como observabilidade, controlabilidade e a possibilidade de falhar. Os testes realizados no sistema apresentado mostraram que a linguagem de controle consegue, mesmo permitindo um nivel de liberdade ao sistema, identificar as falhas verificando somente para os eventos que ocorrem após a ocorrência da mesma. / This work we presents a proposal a software of simulation and fault diagnosis applied to an automation system. In that task was developed , a case study that contains a problem of industrial automation. The study was used as the source for creating the simulation that follows the specifications of software models, where you can observe the evolution of events through its language and diagnose faults when they occur in one of the machines of the plant. The process of fault diagnosis is based on the rules of diagnosticabilidades presented in the literature. The machines, as well as its restrictions are modeled within the software itself, where the structures of each automaton are defined the caracteristics as observability an the possibility of failure. The tests in the system showed that of the language used can allowing identify fails, checking only for events that occorem after the occurence the fails.

Esta tese trata do problema de controle ótimo estocástico de sistemas com saltos Markovianos e ruído multiplicativo a tempo discreto, com horizontes de tempo finito e infinito. A função custo é composta de termos quadráticos e lineares nas variáveis de estado e de controle, com matrizes peso indefinidas. Como resultado principal do problema com horizonte finito, é apresentada uma condição necessária e suficiente para que o problema de controle seja bem posto, a partir da qual uma solução ótima é derivada. A condição e a lei de controle são escritas em termos de um conjunto acoplado de equações de Riccati interconectadas a um conjunto acoplado de equações lineares recursivas. Para o caso de horizonte infinito, são apresentadas as soluções ótimas para os problemas de custo médio a longo prazo e com desconto, derivadas a partir de uma solução estabilizante de um conjunto de equações algébricas de Riccati acopladas generalizadas (GCARE). A existência da solução estabilizante é uma condição suficiente para que tais problemas sejam do tipo bem posto. Além disso, são apresentadas condições para a existência das soluções maximal e estabilizante do sistema GCARE. Como aplicações dos resultados obtidos, são apresentadas as soluções de um problema de otimização de carteiras de investimento com benchmark e de um problema de gestão de ativos e passivos de fundos de pensão do tipo benefício definido, ambos os casos com mudanças de regime nas variáreis de mercado. / This thesis considers the finite-horizon and infinite-horizon stochastic optimal control problem for discrete-time Markov jump with multiplicative noise linear systems. The performance criterion is assumed to be formed by a linear combination of a quadratic part and a linear part in the state and control variables. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. For the finite-horizon problem the main results consist of deriving a necessary and sufficient condition under which the problem is well posed and a optimal control law is derived. This condition and the optimal control law are written in terms of a set of coupled generalized Riccati difference equations interconnected with a set of coupled linear recursive equations. For the infinite-horizon problem a set of generalized coupled algebraic Riccati equations (GCARE) is studied. In this case, a sufficient condition under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution for the GCARE are presented. Moreover, a solution for the discounted and long run average cost problems is presented. The results obtained are applied to solver a portfolio optimization problem with benchmark and a pension fund problem with regime switching.

Orientador: Jose Claudio Geromel / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-10T01:06:21Z (GMT). No. of bitstreams: 1 Fioravanti_AndreRicardo_M.pdf: 793181 bytes, checksum: 6f60b78faabe194cc22f2cc3157f0d90 (MD5) Previous issue date: 2007 / Resumo: Esta dissertação tem par principal objetivo o estudo do problema de projeto de filtros H2 e Hoo de sistemas lineares discretos com parâmetros sujeitos a saltos markovianos. Inicialmente, sob a hipótese de que o parâmetro da cadeia de Markov é mensurável, fornecemos a caracterização de todos os filtros tais que o erro de estimação é limitado por uma norma, produzindo a solução completa do problema de projeto dependente do modo da cadeia. Baseado neste resultado, consideramos o projeto do filtro robusto capaz de lidar com incertezas paramétricas. Em seguida, propomos um procedimento de projeto de filtros sem o conhecimento da cadeia. Todos os problemas de filtragem são expressos em termos de desigualdades matriciais lineares. Os resultados teóricos são ilustrados através de uma aplicação prática que consiste na comunicação de dados através de um canal markoviano / Abstract: This thesis addresses the H2 and Hoo filtering design problem of discrete-time Markov jump linear systems. First, under the assumption that the Markov parameter is measurable, we provide the characterization of all filters such that the estimation errar remains bounded by a given narm leveI, yielding the complete solution of the mode-dependent filtering design problem. Based on this result, a robust filter design to deal with convex bounded parameter uncertainty is considered. In the sequeI, a design procedure for modeindependent filtering design is proposed. All filters are designed by solving linear matrix inequalities. The theory is illustrated by means of a practical example, consisting the data communication through a markovian channel / Mestrado / Automação / Mestre em Engenharia Elétrica

Made available in DSpace on 2016-03-15T19:37:30Z (GMT). No. of bitstreams: 1 Renato Dalto Fanganiello.pdf: 1457160 bytes, checksum: bf6c236fbb03a0209447afecf0831326 (MD5) Previous issue date: 2010-08-03 / Universidade Presbiteriana Mackenzie / Many synchronization methods for chaotic systems have been proposed over the past decades seeking for applications in communications. However, they have not satisfactorily performed when submitted to non-ideal communication channels. In this work, a discrete-time master-slave system based on Wu and Chua's synchronization model is considered. It is shown that it is possible to achieve synchronization under bandwidth limitations imposed by the communication channel by applying a digital filter in the feedback loop reponsible for the generation of the chaotic signal that will be transmitted. Furthermore, an analytical demonstration is presented showing that synchronization is not affected by the presence of digital filter introduced in the communication system. Results of computacional simulations relating the filter's parameters, such as its order and cut-off frequency, to maximum Lyapunov expoent of the transmitter system, which determines if the transmitted signal is chaotic or periodic, are also shown. / No decorrer das últimas décadas, muitos métodos de sincronismo para sistemas caóticos têm sido propostos visando aplicações em comunicações. No entanto, suas performances não têm se mostrado satisfatórias quando submetidos a condições não ideais de canais de transmissão. Neste trabalho considera-se um sistema mestre-escravo de tempo discreto baseado no modelo de sincronismo de Wu e Chua. Mostra-se que é possível atingir o sincronismo, mesmo quando há limitação de largura de banda imposta pelo canal de comunicação, por meio da introdução de um filtro digital que limita o espectro de potência na malha de realimentação responsável pela geração do sinal que será transmitido. Ademais, demonstra-se analiticamente que a presença do filtro digital introduzido no sistema de comunicação não interfere no seu sincronismo. Também são mostrados resultados de simulações computacionais que relacionam os parâmetros do filtro digital introduzido no sistema de comunicação, como ordem e frequência de corte, com o maior expoente de Lyapunov do sistema transmissor, que determina se o sinal transmitido será caótico ou periódico.

The Internet has been more and more intensively used in recent years. Although network infrastructure has been regularly upgraded, and the ability to manage heavy traffic greatly increased, especially on the core networks, congestion never ceases to appear, as the amount of traffic that flow on the Internet seems to be increasing at an even faster rate. Thus, congestion control mechanisms play a vital role in the functioning of the Internet. Active Queue Management (AQM) is a popular type of congestion control mechanism that is implemented on gateways (most notably routers), which can predict and avoid the congestion before it happens. When properly configured, AQMs can effectively reduce the congestion, and alleviate some of the problems such as global synchronisation and unfairness to bursty traffic. However, there are still many problems regarding AQMs. Most of the AQM schemes are quite sensitive to their parameters setting, and these parameters may be heavily dependent on the network traffic profile, which the administrator may not have intensive knowledge of, and is likely to change over time. When poorly configured, many AQMs perform no better than the basic drop-tail queue. There is currently no effective method to compare the performance of these AQM algorithms, caused by the parameter configuration problem. In this research, the aim is to propose a new analytical model, which mainly uses discrete-time queueing theory. A novel transient modification to the conventional equilibrium-based method is proposed, and it is utilised to further develop a dynamic interactive model of responsive traffic and bottleneck queues. Using step-by-step analysis, it represents the bursty traffic and oscillating queue length behaviour in practical network more accurately. It also provides an effective way of predicting the behaviour of a TCP-AQM system, allowing easier parameter optimisation for AQM schemes. Numerical solution using MATLAB and software simulation using NS-2 are used to extensively validate the proposed models, theories and conclusions.

The South African National Defence Force (SANDF) currently requires a system of systems simulation capability for supporting the different phases of a Ground Based Air Defence System (GBADS) acquisition program. A non-distributed, fast-as-possible simulator and its architectural predecessors developed by the Council for Scientific and Industrial Research (CSIR) was able to provide the required capability during the concept and definition phases of the acquisition life cycle. The non-distributed simulator implements a 100Hz logical time Discrete Time System Specification (DTSS) in support of the existing models. However, real-time simulation execution has become a prioritised requirement to support the development phase of the acquisition life cycle. This dissertation is about the ongoing migration of the non-distributed simulator to a practical simulation architecture that supports the real-time requirement. The simulator simulates a synthetic environment inhabited by interacting GBAD systems and hostile airborne targets. The non-distributed simulator was parallelised across multiple Commod- ity Off the Shelf (COTS) PC nodes connected by a commercial Gigabit Eth- ernet infrastructure. Since model reuse was important for cost effectiveness, it was decided to reuse all the existing models, by retaining their 100Hz logical time DTSSs. The large scale and event-based High Level Architecture (HLA), an IEEE standard for large-scale distributed simulation interoperability, had been identified as the most suitable distribution and parallelisation technology. However, two categories of risks in directly migrating to the HLA were iden- tified. The choice was made, with motivations, to mitigate the identified risks by developing a specialised custom distributed architecture. In this dissertation, the custom discrete time, distributed, peer-to-peer, message-passing architecture that has been built by the author in support of the parallelised simulator requirements, is described and analysed. It reports on empirical studies in regard to performance and flexibility. The architecture is shown to be a suitable and cost effective distributed simulator architecture for supporting a speed-up of three to four times through parallelisation of the 100 Hz logical time DTSS. This distributed architecture is currently in use and working as expected, but results in a parallelisation speed-up ceiling irrespective of the number of distributed processors. In addition, a hybrid discrete-time/discrete-event modelling approach and simulator is proposed that lowers the distributed communication and time synchronisation overhead—to improve on the scalability of the discrete time simulator—while still economically reusing the existing models. The pro- posed hybrid architecture was implemented and its real-time performance analysed. The hybrid architecture is found to support a parallelisation speed- up that is not bounded, but linearly related to the number of distributed pro- cessors up to at least the 11 processing nodes available for experimentation. / Dissertation (MSc)--University of Pretoria, 2009. / Computer Science / unrestricted

The present work introduces a methodology to obtain a discrete time state space representation of an electrical network using the nodal [G] matrix of the Electromagnetic Transients Program (EMTP) solution. This is the first time the connection between the EMTP nodal analysis solution and a corresponding state-space formulation is presented. Compared to conventional state space solutions, the nodal EMTP solution is computationally much more efficient. Compared to the phasor solutions used in transient stability analysis, the proposed approach captures a much wider range of eigenvalues and system operating states. A fundamental advantage of extracting the system eigenvalues directly from the EMTP solution is the ability of the EMTP to follow the characteristics of nonlinearities. The system's trajectory can be accurately traced and the calculated eigenvalues and eigenvectors correctly represent the system's instantaneous dynamics. In addition, the algorithm can be used as a tool to identify network partitioning subsystems suitable for real-time hybrid power system simulator environments, including the implementation of multi-time scale solutions. The proposed technique can be implemented as an extension to any EMTP-based simulator. Within our UBC research group, it is aimed at extending the capabilities of our real-time PC-cluster Object Virtual Network Integrator (OVNI) simulator. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate