Optimization can contribute significantly both to on- line control and to the design of linear and nonlinear controllers. In the form of receding horizon control, it has the potential, not easily provided by other methods, to stabilize linear and nonlinear systems with state and control constraints. When employed in an interactive, optimization-based design environment, it enables control systems to be designed to achieve the diverse, possibly conflicting, objectives that typify engineering design. The purpose of this research is twofold. Firstly, it will endeavour to provide a firm basis for the use of receding horizon control by a comprehensive program of research aimed at: (i) reducing substantially the on-line computational demands made by existing, stabilizing receding horizon controllers, (ii) developing receding horizon observers for use when the state is not accessible, (iii) developing adaptive receding horizon control for the case when the plant is unknown, and (iv) exploring the use of optimization-based design to achieve these objectives. Secondly, it aims to improve computational tools for optimization-based design by research on: (i) semi- infinite optimization, (ii) global optimization, (iii) semi-infinite global optimization, and, (iv) simple, robust optimal control algorithms for use in receding horizon control.
