UBC Theses and Dissertations
Decomposition and optimal control theory Masak, Mart
The objective of this thesis is to investigate decomposition and its applicability to the theory of optimal control. The work begins with a representation of the structure of the optimal control problem in terms of directed graphs. This representation exposes a strong connectedness property leading to fundamental difficulties which are central in limiting the class of control problems to which decomposition can successfully be applied. Computational problems of optimal control are then considered, and decomposition is found to provide a framework within which to analyse numerical methods suitable for parallel processing. A number of such methods are shown and a numerical example is used to illustrate the viability of one of these. In the second part of the thesis, the optimal control law synthesis problem is discussed together with an inverse problem. The latter concerns the requirement of a second-level co-ordinator in a hierarchical structure. A multi-level controller is then suggested for a class of systems. The effect of this controller structure is to provide a performance very close to the optimal while maintaining adequate sub-optimal control in case of a breakdown of the second-level co-ordinator. The structure is justified on the basis of the second variation theory of the calculus of variations. Finally, a new computational technique founded on the geometrical concepts of optimal control theory is introduced. This results in replacing the unstable co-state variables associated with Pontryagin's maximum principle with a set of bounded variables. The facility in the choice of initial iterates makes the method promising.
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