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<p> Ten different reduced models, of a particular test system are selected. Two cost functions are selected and the test system minimum cost is found for each. The model optimal controls are found for each cost function and are used to provide sub-optimal control of the system using two different methods. The system cost is calculated for each case and compared to the minimum attainable. The reduction methods are compared with a view to application for the near-optimal control of a linear system.</p> / Thesis / Master of Engineering (MEngr)

Cancer is a generic term for a large group of diseases where cells of the body lose their normal mechanisms for growth so that they grow in an uncontrolled way. One of the most common treatments of cancer is chemotherapy that aims to kill abnormal proliferating cells; however normal cells and other organs of the patients are also adversely affected. In practice, it's often difficult to maintain optimum chemotherapy doses that can maximise the abnormal cell killing as well as reducing side effects. The most chemotherapy drugs used in cancer treatment are toxic agents and usually have narrow therapeutic indices, dose levels in which these drugs significantly kill the cancerous cells are close to the levels which sometime cause harmful toxic side effects. To make the chemotherapeutic treatment effective, optimum drug scheduling is required to balance between the beneficial and toxic side effects of the cancer drugs. Conventional clinical methods very often fail to find drug doses that balance between these two due to their inherent conflicting nature. In this investigation, mathematical models for cancer chemotherapy are used to predict the number of tumour cells and control the tumour growth during treatment. A feedback control method is used so as to maintain certain level of drug concentrations at the tumour sites. Multi-objective Genetic Algorithm (MOGA) is then employed to find suitable solutions where drug resistances and drug concentrations are incorporated with cancer cell killing and toxic effects as design objectives. Several constraints and specific goal values were set for different design objectives in the optimisation process and a wide range of acceptable solutions were obtained trading off among different conflicting objectives. Abstract v In order to develop a multi-objective optimal control model, this study used proportional, integral and derivative (PID) and I-PD (modified PID with Integrator used as series) controllers based on Martin's growth model for optimum drug concentration to treat cancer. To the best of our knowledge, this is the first PID/I-PD based optimal chemotherapy control model used to investigate the cancer treatment. It has been observed that some solutions can reduce the cancer cells up to nearly 100% with much lower side effects and drug resistance during the whole period of treatment. The proposed strategy has been extended for more drugs and more design constraints and objectives.

We investigate the impact of cash reserves upon the optimal behaviour of a modelled firm that has uncertain future revenues. To achieve this, we build up a corporate financing model of a firm from a Real Options foundation, with the option to close as a core business decision maintained throughout. We model the firm by employing an optimal stochastic control mathematical approach, which is based upon a partial differential equations perspective. In so doing, we are able to assess the incremental impacts upon the optimal operation of the cash constrained firm, by sequentially including: an optimal dividend distribution; optimal equity financing; and optimal debt financing (conducted in a novel equilibrium setting between firm and creditor). We present efficient numerical schemes to solve these models, which are generally built from the Projected Successive Over Relaxation (PSOR) method, and the Semi-Lagrangian approach. Using these numerical tools, and our gained economic insights, we then allow the firm the option to also expand the operation, so they may also take advantage of favourable economic conditions.

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No / A novel threefold optimization algorithm is proposed to simultaneously solve the nonlinear model predictive control and dynamic real-time optimization for batch processes while optimizing the batch operation time. Object-oriented programming and parallel computing are exploited to make the algorithm effective to handle industrial cases. A well-known literature case is selected to validate the algorithm.

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In order to have an interception with a target, a missile should be guided with a successful guidance algorithm accompanied with a suitable autopilot structure. In this study, different autopilot and guidance designs for a canard-controlled missile are developed. As a first step, nonlinear missile mathematical model is derived by using the equations of motion with aerodynamic coefficients found by Missile DATCOM program. Autopilot design starts by the linearization of the nonlinear missile model around equilibrium flight conditions. Controllers based on the concepts of optimal control theory results and sliding mode control are designed. In all of the designs, angle of attack command and roll angle command type autopilot structures are used. During the design process, variations in angle of attack, Mach number and altitude can lead to significant performance degradation. This problem is typically solved by applying gain-scheduling methodology according to these parameters. There are different types of guidance methods in the literature. Throughout this study, proportional navigation guidance and its modified forms are selected as a base algorithm in the guidance system design. Other robust forms of guidance methods, such as an optimal guidance approach and sliding mode guidance, are also formed for performance comparison with traditional proportional navigation guidance approach. Finally, a new guidance method, optimal proportional-integral guidance, whose performance is the best among all of the methods included in the thesis against highly maneuvering targets, is introduced.

[pt] O controle ativo de vibrações consiste na supressão ou atenuação das vibrações mediante a adição deliberada de forças de controle ao sistema. O controle ativo de vibrações tem um grande interesse na indústria aeroespacial devido às restrições de peso. As técnicas de controle ótimo não são propícias quando se tem dinâmica não-modelada, incertezas paramétricas e ambientes ruidosos, como é o caso na indústria aeroespacial. Assim, as técnicas de controle robusto parecem mais adequadas. A procura da maior família de perturbações em torno de uma dada planta nominal estabilizável por um único contro-lador em malha fechada pode ser formulada como o problema de controle H 1 . De fato,para muitos problemas de controle que requerem bons desempenhos, como por exemplo,controle de grandes sistemas espaciais, o controle ótimo robusto (controle H2=H 1 ) é um dos que assegura a robustez em estabilidade e o desempenho ótimo requerido. O presente trabalho considera o problema de atenuação de distúrbios para uma viga flexível simplesmente apoiada. A viga é modelada como um sistema de parâmetros concentrados. Um procedimento é estabelecido de forma que se leve em conta o desempenho da viga controlada e a robustez em estabilidade do sistema controlado. O problema de controle foi formulado em um contexto hilbertiano que permitiu garantir a existência (e unicidade) da solução. Uma aproximação do controlador é calculada através de uma pro- jeção da solução em um espaço de dimensão finita gerado pelo método de Galerkin considerando-se funções racionais como base para um espaço de Hardy ponderado. Resultados da aplicação indicam que o desempenho é fortemente relacionado à estabilidade. Existe um compromisso entre estabilidade e desempenho. / [es] EL control activo de vibraciones consiste en suprimir o atenuar las vibraciones adicionando deliberadamente fuerzas de control al sistema. El control activo de vibraciones levanta gran interés en la industria aeroespacial debido a las restricciones de peso. Las técnicas de control óptimo no son propicias cuando se tiene una dinámica no modelada, errores paramétricas y ambientes ruidosos, como es el caso en la industria aeroespacial. Así, las técnicas de control robusto parecen más adecuadas. La búsqueda de la mayor familia de perturbaciones en torno a una planta nominal, estabilizable por un único controlador en malla cerrada puede ser formulada como el problema de control H1. De hecho, para muchos problemas de control es necesario un buen desempeño, como por ejemplo, el control de grandes sistemas espaciales, el control óptimo robusto (control H2=H1 ) es uno de los que asegura la robustez en estabilidad y el desempeño óptimo requerido. El presente trabajo considera el problema de atenuación de disturbios para una viga flexible simplemente apoyada, modelando la viga como un sistema de parámetros concentrados. Se establece un procedimiento que considera el desempeño de la viga controlada y la robustez en estabilidad del sistema. El problema de control fue formulado en un contexto hilbertiano, lo que permitió garantizar la existencia (y unicidad) de la solución. Posteriormente, se calcula una aproximación del controlador a través de una proyección de la solución en un espacio de dimensión finita generado por el método de Galerkin considerando funciones racionales como base para un espacio de Hardy ponderado. Los resultados de la aplicación indican que el desempeño está fuertemente relacionado con la estabilidad. Existe un compromiso entre estabilidad y desempeño.