In this thesis I develop a mathematical model for an apartment building during an earthquake. The movement of the building is restricted to a plane and twisting motions have been assumed negligible. A control system for the building is developed using optimal control techniques. For a quadratic objective functional, the existence of an optimal control is determined and numerical results are generated that show that the controller significantly lowers the chaotic oscillations in the building. The numerical work was done with the Miser3 package for Matlab. Relaxation of different constraints are considered, including multiple controls, varying stories, and different objective functionals.

<p>The main achievement of this work is the development of a duality theory for optimal control problems with stochastic differential equations. Incipient with the Hamilton-Jacobi-Bellman equation we established a dual problem to a given stochastic control problem and were also able to generalise the assembled theory.</p>

The main achievement of this work is the development of a duality theory for optimal control problems with stochastic differential equations. Incipient with the Hamilton-Jacobi-Bellman equation we established a dual problem to a given stochastic control problem and were also able to generalise the assembled theory.

Mathematical models often involve unknown parameters that must be fit to experimental data. These so-called parameter estimation problems have many applications that may involve differential equations, optimization, and control theory. EASY-FIT and SOCS are two software packages that solve parameter estimation problems. In this thesis, we discuss the design and implementation of a source-to-source translator called EFtoSOCS used to translate EASY FIT input into SOCS input. This makes it possible to test SOCS on a large number of parameter estimation problems available in the EASY-FIT problem database that vary both in size and difficulty.<p>Parameter estimation problems typically have many locally optimal solutions, and the solution obtained often depends critically on the initial guess for the solution. A 3-stage approach is followed to enhance the convergence of solutions in SOCS. The stages are designed to use an initial guess that is progressively closer to the optimal solution found by EASY-FIT. Using this approach we run EFtoSOCS on all translatable problems (691) from the EASY-FIT database. We find that all but 7 problems produce converged solutions in SOCS. We describe the reasons that SOCS was not able solve these problems, compare the solutions found by SOCS and EASY-FIT, and suggest possible improvements to both EFtoSOCS and SOCS.

Mathematical models often involve unknown parameters that must be fit to experimental data. These so-called parameter estimation problems have many applications that may involve differential equations, optimization, and control theory. EASY-FIT and SOCS are two software packages that solve parameter estimation problems. In this thesis, we discuss the design and implementation of a source-to-source translator called EFtoSOCS used to translate EASY FIT input into SOCS input. This makes it possible to test SOCS on a large number of parameter estimation problems available in the EASY-FIT problem database that vary both in size and difficulty.<p>Parameter estimation problems typically have many locally optimal solutions, and the solution obtained often depends critically on the initial guess for the solution. A 3-stage approach is followed to enhance the convergence of solutions in SOCS. The stages are designed to use an initial guess that is progressively closer to the optimal solution found by EASY-FIT. Using this approach we run EFtoSOCS on all translatable problems (691) from the EASY-FIT database. We find that all but 7 problems produce converged solutions in SOCS. We describe the reasons that SOCS was not able solve these problems, compare the solutions found by SOCS and EASY-FIT, and suggest possible improvements to both EFtoSOCS and SOCS.

Wind energy is the most abundant resource in the renewable energy portfolio. Increasing the wind capture capability improves the economic viability of this technology, and makes it more competitive with traditional fossil-fuel based supplies. Therefore, it is necessary to explore control strategies that maximize aerodynamic efficiency, thus, the wind energy capture. Several control algorithms are developed and compared during this research. A traditional feedback control is adapted as the benchmark approach, where the turbine torque and the blade pitch angle are used to control the wind turbine operation during partial and full load operations, correspondingly. Augmented feedback control algorithms are then developed to improve the wind energy harvesting. Optimal control methodologies are extensively explored to achieve maximal wind energy capture. Numerical optimization techniques, such as direct shooting optimization are employed. The direct shooting method convert the optimal control problem into a parameter optimization problem and use nonlinear programming algorithm to find the optimal solution. The dynamic programming, a global optimization approach over a time horizon, is also investigated. The dynamic programming finds the control inputs for the blade pitch angle and speed ratio to maximize the power coefficient, based on historical wind data. A dynamic wind turbine model has been developed to facilitate this process by characterizing the performance of the various possible input scenarios. Simulation results of each algorithm on real wind site data are presented to compare the wind energy capture under the proposed control algorithms with the traditional feedback control design. The result of the tradeoff analysis between the computation expense and the energy capture is also reported. / text

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