A pitch-control predictor-corrector ascent guidance algorithm has been developed and evaluated for a rocket-based upper stage of a two-stage-to-orbit launch vehicle. Detailed descriptions of the predictor-corrector algorithm and a neural network loop modification are given. The mission requirement is insertion into a stable 50 x 100 nmi orbit at 375,000 ft altitude, coasting toward apogee at a positive inertial flight path angle. Three degree-of-freedom trajectory analysis is performed using the Program to Optimize Simulated Trajectories (POST2). Results of Monte Carlo simulations including uncertainties in atmosphere, thrust, aerodynamics and initial state are presented and compared to trajectories optimized for maximum injected weight. / Master of Science

Orientador: Aurelio Ribeiro Leite de Oliveira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-24T06:40:02Z (GMT). No. of bitstreams: 1 SunaguaSalgado_Porfirio_D.pdf: 2121161 bytes, checksum: 6d961fd2da8ded7cbc0733d9f190497a (MD5) Previous issue date: 2014 / Resumo: Uma abordagem do método preditor-corretor de Mehrotra para resolver problemas de programação linear de grande porte, que utiliza uma classe do precondicionador separador, para resolver sistemas lineares envolvidos por métodos iterativos precondicionados, necessita de uma base que é encontrada por um sofisticado processo de fatoração LU retangular da matriz de restrições. O precondicionador separador tem bom desempenho perto de uma solução ótima, onde as matrizes envolvidas ficam muito mal condicionadas. Neste trabalho, primeiro desenvolvemos o método preditor-corretor com o parâmetro de penalização a fim de reduzir o mau condicionamento da matriz de equações normais. O sucesso desta abordagem é garantido pela demonstração do teorema de convergência de penalização mista com o parâmetro de barreira. Em seguida, implementamos uma nova abordagem para encontrar uma base para o precondicionador separador mediante um processo de fatoração LU retangular padrão aplicada à matriz transposta de restrições escalada. Na maioria das vezes, esta base encontrada é melhor condicionada que a base do método de fatoração retangular anterior. Testes computacionais comprovam uma redução da média do número de iterações do método de gradientes conjugados precondicionado. Também, a eficácia e a robustez da nova abordagem é comprovada por conseguir uma melhor curva de desempenho / Abstract: The class of splitting preconditioners for the iterative solution of linear systems arising from Mehrotra's predictor-corrector method for large-scale linear programming problems needs to find a base by a sophisticated process based upon applying a rectangular LU factorization. The class of splitting preconditioners works better near a solution of the linear programming problems when the matrices are highly ill-conditioned. In this work, we develop the penalty parameter in Mehrotra's predictor-corrector method in order to reduce the ill-conditioning of the normal equations matrix. The success of this approach is guaranteed by the proof of the theorem of convergence of mixed penalty with the barrier parameter. In addition, we develop and implement a new approach to find a basis for the splitting preconditioner, based upon standard rectangular LU factorization with partial permutation of the transpose of the scaled linear programming constraint matrix. In most cases, the basis is better conditioned than the existing one. Computational tests show a reduction in the average number of iterations of the preconditioned conjugate gradient method. Also, the efficiency and robustness of the new approach is demonstrated by achieving better performance profile / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

The ¡§Congestion Management¡¨ (CM) always has been an outstanding and major problem in power system operation. To solve this problem, experts compose solutions in a wide variety. This thesis, based on the equivalent current, applies the Equivalent Current Injection (ECI) concept and circuit parameters to derive the Power Flow Tracing Method (PFTM) . By means of this method we can get a Sensitive Matrix (SM), which is also called the Contribution Matrix (CM), to show the linear relationship between the input power and tidal current discharge of each generator set, with the linear relationship we can derive the mathematic model of treating the congestion problem discussed in this thesis. Combining the Predictor-Corrector Interior Point Algorithm (PCIPA), we can manipulate the change of each generator set in the prospective of solving the congestion problem resulting from the system contingency (SC). The thesis performed various simulations for the IEEE 30 Bus system. Regarding the power contingencies, the solutions of the power-congestion problems can be resulted from the following incidents: heavy load addition, transmission line tripped, generator malfunction as well as the multi-contingencies, etc., which can all be solved with solutions within reasonably restricted domains. We can thus verify the effectiveness of the method .

With the deregulation of power industry and the market competition, low cost, reliable power supply, and secured system operations are major concerns of the advanced deregulation markets. Power system protection is important for service reliability and quality assurance. To reduce the outage duration and promptly restore power services, fault section estimate has to be done effectively and accurately with fault alarms. First, an operational strategy for secondary power system restoration using Modified Grey Relational Analysis (MGRA) is proposed. The Restoration Scheme (RS) can be divided into three steps involving fault section determination, recovering process, and voltage correction process. Three GRAs are incorporated to design the overall restoration scheme. The first GRA uses network switching status to identify the fault. The second GRA combines switching states and load levels for network recovery. The third GRA uses capacitor bank control to support bus voltages. For security operation of restoration scheme, an Equivalent Current Injection (ECI) based hybrid current-power Optimal Power Flow (OPF) model with Predictor-Corrector Interior Point Algorithm (PCIPA) is used to verify the proposed scheme by off-line analysis to confirm a secure overall network operation including load-power balance, power generation limits, voltage limits, and power flow limits. The proposed method can further decompose into two sub-problems. Computer simulations were conducted with an IEEE 30-bus power system to show the effectiveness of the proposed restoration scheme and the PCIPA technique is very accurate, robust, and efficient for the modified OPF solution.

Stochastic differential equations (SDE’s) are used to describe systems which are influenced by randomness. Here, randomness is modelled as some external source interacting with the system, thus ensuring that the stochastic differential equation provides a more realistic mathematical model of the system under investigation than deterministic differential equations. The behaviour of the physical system can often be described by probability and thus understanding the theory of SDE’s requires the familiarity of advanced probability theory and stochastic processes. SDE’s have found applications in chemistry, physical and engineering sciences, microelectronics and economics. But recently, there has been an increase in the use of SDE’s in other areas like social sciences, computational biology and finance. In modern financial practice, asset prices are modelled by means of stochastic processes. Thus, continuous-time stochastic calculus plays a central role in financial modelling. The theory and application of interest rate modelling is one of the most important areas of modern finance. For example, SDE’s are used to price bonds and to explain the term structure of interest rates. Commonly used models include the Cox-Ingersoll-Ross model; the Hull-White model; and Heath-Jarrow-Morton model. Since there has been an expansion in the range and volume of interest rate related products being traded in the international financial markets in the past decade, it has become important for investment banks, other financial institutions, government and corporate treasury offices to require ever more accurate, objective and scientific forms for the pricing, hedging and general risk management of the resulting positions. Similar to ordinary differential equations, many SDE’s that appear in practical applications cannot be solved explicitly and therefore require the use of numerical methods. For example, to price an American put option, one requires the numerical solution of a free-boundary partial differential equation. There are various approaches to solving SDE’s numerically. Monte Carlo methods could be used whereby the physical system is simulated directly using a sequence of random numbers. Another method involves the discretisation of both the time and space variables. However, the most efficient and widely applicable approach to solving SDE’s involves the discretisation of the time variable only and thus generating approximate values of the sample paths at the discretisation times. This paper highlights some of the various numerical methods that can be used to solve stochastic differential equations. These numerical methods are based on the simulation of sample paths of time discrete approximations. It also highlights how these methods can be derived from the Taylor expansion of the SDE, thus providing opportunities to derive more advanced numerical schemes. / Dissertation (MSc (Mathematics of Finance))--University of Pretoria, 2007. / Mathematics and Applied Mathematics / MSc / unrestricted

Master of Science

Orientador: Antonio Roberto Balbo / Banca: Márcia Marcondes Altimari Samed / Banca: Edmea Cassia Baptista / Resumo: Este trabalho visa a investigação e implementação de métodos Primal - Dual Previsor-Corretor de Pontos Interiores com a estratégia de busca unidimensional, e a aplicação destes em problemas de Despacho Econômico e Ambiental. Objetiva-se utilizar estes métodos para determinar soluções aproximadas e consistentes dos problemas causados citados, que forneçam a solução de minimização dos custos dos combustíveis empregados na geração termoelétrica de energia, otimizando um processo de alocação da demanda de energia elétrica entre as unidades geradoras disponíveis, de tal forma que as restrições operacionais sejam atendidas e que o custo de geração é minimizado. Pretende-se também, analisar o problema de Despacho Ambiental com um objetivo único quando se acopla a este o Problema de Despacho Econômico e busca-se, simultaneamente, a minimização dos custos de geração e a redução da emissão de poluentes na natureza. Os métodos foram implementados, testados em Problemas de Despacho Econômico e Ambiental, e o seu desempenho foi comparado com outros métodos já utilizados, cujos resultados são encontrados na literatura / Abstract: This work aims the investigation and implementation of Primal-Dual Predictor-Corrector interior points methods, with the strategy of one-dimensional search, and its application in Economic and Environmental Dispatch Problems. It pretends to use these methods to determine approximate and consistent solutions of the mentioned problems, that provide the solution to minimize the fuel costs used in thermoelectric power generation, optimizing an allocations process of eletric power demand among available generation units, such that the operational constraints are attended and that generation cost is minimized. It too pretends to analyze the Environmental Dispatch Problem with the one objective when it is joined with the Dispatch Problems and it searchs, simultaneously, the minimization of the generation costs and the reduction of emission of the polluants in the nature. The methods were implemented, tested on the Economic and Environemental Dispatch Problems and its performance was compared with others method currently used, whose results are found in the literature / Mestre

Neste trabalho, os métodos de pontos interiores primal-dual e preditor corretor são estudados e desenvolvidos para o problema de minimização de custos na geração e perdas na transmissão do pré-despacho DC (fluxo de carga em corrente contínua) de um sistema de potência hidroelétrico, com base no modelo de fluxo em redes e no princípio do mínimo esforço. A estrutura matricial, resultante da simplificação do problema proposto pela inclusão do princípio do mínimo esforço, é estudada visando implementações eficientes. / In this work, the primal-dual and predictor corrector interior points methods are studied and developed for the predispatch DC problem that minimizes generation and transmission losses on hydroelectric power systems, on the basis of the network flow model and the minimum effort principle. The matrix structure, resulting of the simplification of the problem considered by inclusion of the minimum effort principle, is studied aiming efficient implementations. A disturbed primal-dual method is considered on the basis of a heuristic definition that determine the choice of the disturbance parameter. This method showed to be efficient in practice and converged in fewer iterations when compare with an existing implementation of the network flow model.

Orientadores: Sandra Augusta Santos, Roberto Andreani / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-14T11:40:11Z (GMT). No. of bitstreams: 1 Shirabayashi_WesleyVagnerInes_D.pdf: 877226 bytes, checksum: a814cd9947431a0aee17517c4cc953f4 (MD5) Previous issue date: 2009 / Resumo: Neste trabalho reformulamos o problema de complementaridade não linear generalizado (GNCP) em cones poliedrais como um sistema não linear com restrição de não negatividade em algumas variáveis, e trabalhamos na resolução de tal reformulação por meio de estratégias de pontos interiores. Em particular, definimos dois algoritmos e provamos a convergência local de tais algoritmos sob hipóteses usuais. O primeiro algoritmo é baseado no método de Newton, e o segundo, no método tensorial de Chebyshev. O algoritmo baseado no método de Chebyshev pode ser visto como um método do tipo preditor-corretor. Tal algoritmo, quando aplicado a problemas em que as funções envolvidas são afins, e com escolhas adequadas dos parâmetros, torna-se o bem conhecido algoritmo preditor-corretor de Mehrotra. Também apresentamos resultados numéricos que ilustram a competitividade de ambas as propostas. / Abstract: In this work we reformulate the generalized nonlinear complementarity problem (GNCP) in polyhedral cones as a nonlinear system with nonnegativity in some variables and propose the resolution of such reformulation through interior-point methods. In particular we define two algorithms and prove the local convergence of these algorithms under standard assumptions. The first algorithm is based on Newton's method and the second, on the Chebyshev's tensorial method. The algorithm based on Chebyshev's method may be considered a predictor-corrector one. Such algorithm, when applied to problems for which the functions are affine, and the parameters are properly chosen, turns into the well-known Mehrotra's predictor corrector algorithm. We also present numerical results that illustrate the competitiveness of both proposals. / Doutorado / Otimização / Doutor em Matemática Aplicada

Neste trabalho, os métodos de pontos interiores primal-dual e preditor corretor são estudados e desenvolvidos para o problema de minimização de custos na geração e perdas na transmissão do pré-despacho DC (fluxo de carga em corrente contínua) de um sistema de potência hidroelétrico, com base no modelo de fluxo em redes e no princípio do mínimo esforço. A estrutura matricial, resultante da simplificação do problema proposto pela inclusão do princípio do mínimo esforço, é estudada visando implementações eficientes. / In this work, the primal-dual and predictor corrector interior points methods are studied and developed for the predispatch DC problem that minimizes generation and transmission losses on hydroelectric power systems, on the basis of the network flow model and the minimum effort principle. The matrix structure, resulting of the simplification of the problem considered by inclusion of the minimum effort principle, is studied aiming efficient implementations. A disturbed primal-dual method is considered on the basis of a heuristic definition that determine the choice of the disturbance parameter. This method showed to be efficient in practice and converged in fewer iterations when compare with an existing implementation of the network flow model.