Leer

No description available.

Leer

Linear feedback control is considered for large systems of differential algebraic equations arising from discretization of saddle point problems. Necessary conditions are derived by applying the Maximum Principle and have the form of constrained Riccati equations. We consider two approaches for solving the feedback control problem as well as practical numerical methods. Numerical studies using examples derived from a constrained heat equation and Stokes equation confirms the effectiveness of the approaches we consider. / Master of Science

This research focuses on the development of a solution strategy for the optimization of large-scale dynamic systems under uncertainty. Uncertainty resides naturally within the external forces posed to the system or from within the system itself. For example, in chemical process systems, external inputs include flow rates, temperatures or compositions; while internal sources include kinetic or mass transport parameters; and empirical parameters used within thermodynamic correlations and expressions. The goal in devising a dynamic optimization approach which explicitly accounts for uncertainty is to do so in a manner which is computationally tractable and is general enough to handle various types and sources of uncertainty. The approach developed in this thesis follows a so-called multiperiod technique whereby the infinite dimensional uncertainty space is discretized at numerous points (known as periods or scenarios) which creates different possible realizations of the uncertain parameters. The resulting optimization formulation encompasses an approximated expected value of a chosen objective functional subject to a dynamic model for all the generated realizations of the uncertain parameters. The dynamic model can be solved, using an appropriate numerical method, in an embedded manner for which the solution is used to construct the optimization formulation constraints; or alternatively the model could be completely discretized over the temporal domain and posed directly as part of the optimization formulation. Our approach in this thesis has mainly focused on the embedded model technique for dynamic optimization which can either follow a single- or multiple-shooting solution method. The first contribution of the thesis investigates a combined multiperiod multiple-shooting dynamic optimization approach for the design of dynamic systems using ordinary differential equation (ODE) or differential-algebraic equation (DAE) process models. A major aspect of this approach is the analysis of the parallel solution of the embedded model within the optimization formulation. As part of this analysis, we further consider the application of the dynamic optimization approach to several design and operation applications. Another vmajor contribution of the thesis is the development of a nonlinear programming (NLP) solver based on an approach that combines sequential quadratic programming (SQP) with an interior-point method (IPM) for the quadratic programming subproblem. A unique aspect of the approach is that the inherent structure (and parallelism) of the multiperiod formulation is exploited at the linear algebra level within the SQP-IPM nonlinear programming algorithm using an explicit Schur-complement decomposition. Our NLP solution approach is further assessed using several static and dynamic optimization benchmark examples. / Thesis / Doctor of Philosophy (PhD)

En el extremo sureste del Perú (Arequipa, Cusco y Puno), entre la Cordillera Occidental y el Altiplano, se extiende una cadena de montañas denominada Complejo Volcánico Sillapaca, formación geológica conformada principalmente por lavas de composición andesítica. Este complejo ha experimentado colapsos o derrumbes cuyos depósitos son denominados avalanchas de escombros, eventos altamente destructivos que modificaron la morfología del terreno. Estos depósitos de avalanchas de escombros (DAE) son observados en los distritos de Santa Lucía y Cabanillas, provincia de Lampa y San Román, respectivamente, región Puno. Ahí se cartografiaron y delimitaron tres depósitos de avalanchas de escombros, en los sectores Puncune, Laripata y Quimsachata, así como las zonas de arranque o fuente de dichos depósitos, que abarcan un área de 30 km2 del total de la zona de estudio (200 km2). Se estimaron volúmenes de 0,9, 0,55 y 0,74 km3 para los DAE de Puncune, Laripata y Quimsachata, respectivamente. Se infiere que las avalanchas de escombros pudieron haberse originado por la combinación de varios factores que incluyen: (i) inyección de magma de composición diorítica porfirítica emplazado en la parte sur de los depósitos; (ii) desestabilización del edificio por crecimiento y sobrepresurización de domos de composición monzodiorítica, y (iii) paleosismos en algunas de las fallas del sistema Cusco-Lagunillas. / En el extremo sureste del Perú (Arequipa, Cusco y Puno), entre la Cordillera Occidental y el Altiplano, se extiende una cadena de montañas denominada Complejo Volcánico Sillapaca, formación geológica conformada principalmente por lavas de composición andesítica. Este complejo ha experimentado colapsos o derrumbes cuyos depósitos son denominados avalanchas de escombros, eventos altamente destructivos que modificaron la morfología del terreno. Estos depósitos de avalanchas de escombros (DAE) son observados en los distritos de Santa Lucía y Cabanillas, provincia de Lampa y San Román, respectivamente, región Puno. Ahí se carto- grafiaron y delimitaron tres depósitos de avalanchas de escombros, en los sectores Puncune, Laripata y Quimsachata, así como las zonas de arranque o fuente de dichos depósitos, que abarcan un área de 30 km2 del total de la zona de estudio (200 km2). Se estimaron volúmenes de 0,9, 0,55 y 0,74 km3 para los DAE de Puncune, Laripata y Quimsachata, respectivamente. Se infiere que las avalanchas de escombros pudieron haberse originado por la combinación de varios factores que incluyen: (i) inyección de magma de composición diorítica porfirítica emplazado en la parte sur de los depósitos; (ii) desestabilización del edificio por crecimiento y sobrepresurización de domos de composición monzodiorítica, y (iii) paleosismos en algunas de las fallas del sistema Cusco-Lagunillas.

Degree awarded with distinction on 11 December 1997 'n Verhandeling ingelewer ter voldoening aan die vereistes vir die graad Magister Artium in die Departement van Afrikaans en Nederlands by die Universiteit van die Witwatersrand. Johannesburg, 1997 / This dissertation investigates the canonized criticism on Etienne Leroux's Sewe dee by die S'ilbersteins (1962) from the time of the novel's publication up to the 1980's. The most important analytical strategies that were implemented in this period become, in themselves, the topic of research. The study at hand claims that the allegorical structure of the novel, wi th its subsequent distinction between surface and substructure leads to irreconcilable re&dfngs. The critics either link the view of life presented b~ the novel to a limited number of imtedded fields of reference, or they present all of these fields without questioning any conflicting claims to truth. In this dissertation the novel is approached from an existentialist perspective from which all claims to truth are relativised, and the focus shifts to the narrative itself. This reading strategy departs to a large extent from existing approaches that concentrate on the substructure.

In this thesis, different topics for models that consist of both differential and algebraic equations are studied. The interest in such models, denoted DAE models, have increased substantially during the last years. One of the major reasons is that several modern object-oriented modeling tools used to model large physical systems yield models in this form. The DAE models will, at least locally, be assumed to be described by a decoupled set of ordinary differential equations and purely algebraic equations. In theory, this assumption is not very restrictive because index reduction techniques can be used to rewrite rather general DAE models to satisfy this assumption. One of the topics considered in this thesis is optimal feedback control. For state-space models, it is well-known that the Hamilton-Jacobi-Bellman equation (HJB) can be used to calculate the optimal solution. For DAE models, a similar result exists where a Hamilton-Jacobi-Bellman-like equation is solved. This equation has an extra term in order to incorporate the algebraic equations, and it is investigated how the extra term must be chosen in order to obtain the same solution from the different equations. A problem when using the HJB to find the optimal feedback law is that it involves solving a nonlinear partial differential equation. Often, this equation cannot be solved explicitly. An easier problem is to compute a locally optimal feedback law. For analytic nonlinear time-invariant state-space models, this problem was solved in the 1960's, and in the 1970's the time-varying case was solved as well. In both cases, the optimal solution is described by convergent power series. In this thesis, both of these results are extended to analytic DAE models. Usually, the power series solution of the optimal feedback control problem consists of an infinite number of terms. In practice, an approximation with a finite number of terms is used. A problem is that for certain problems, the region in which the approximate solution is accurate may be small. Therefore, another parametrization of the optimal solution, namely rational functions, is studied. It is shown that for some problems, this parametrization gives a substantially better result than the power series approximation in terms of approximating the optimal cost over a larger region. A problem with the power series method is that the computational complexity grows rapidly both in the number of states and in the order of approximation. However, for DAE models where the underlying state-space model is control-affine, the computations can be simplified. Therefore, conditions under which this property holds are derived. Another major topic considered is how to include stochastic processes in nonlinear DAE models. Stochastic processes are used to model uncertainties and noise in physical processes, and are often an important part in for example state estimation. Therefore, conditions are presented under which noise can be introduced in a DAE model such that it becomes well-posed. For well-posed models, it is then discussed how particle filters can be implemented for estimating the time-varying variables in the model. The final topic in the thesis is model reduction of nonlinear DAE models. The objective with model reduction is to reduce the number of states, while not affecting the input-output behavior too much. Three different approaches are studied, namely balanced truncation, balanced truncation using minimization of the co-observability function and balanced residualization. To compute the reduced model for the different approaches, a method originally derived for nonlinear state-space models is extended to DAE models.

Thesis (Ph. D.)--University of South Carolina, 2004. / Includes bibliographical references (leaves 194-212).

This dissertation introduces a Korean composer, Isang Yun (1917-1995), who embraced European traditions but retained Asian characteristics in his compositions. Attending the 1958 summer course in Darmstadt in Germany, Yun was strongly influenced by the avant-garde style of Boulez, Stockhausen, Nono, and Cage. In addition to his work as a composer, Yun distinguished himself, as one of the most important Asian composers to blend Eastern and Western music; and although his musical training focused on Western music, he continued the pursuit of Eastern sounds and philosophies throughout his musical life. Imprisoned in 1967 by the South Korean government, Isang Yun's music, particularly in later life, incorporates his beliefs on social and political issues together with musical ideas. Although his love of country was deep, Isang Yun was not allowed to return to South Korea, and he lived in Germany for the remainder of his professional life. In this study, my purpose is to investigate the development of Yun's musical ideas from his acceptance of Taoism four structures in the world: the Tao, heaven, earth, and man. The presence of both Western and Eastern influences in Yun's music provides the basic of his musical style, and analysis of Salomo für Altoflöte oder Flöte is included in this dissertation.