Abstract. An abstract hierarchical control theory is developed for discrete-event systems, based on the concepts of control structures and observers. Control structure is an abstract generalization of the family of controllable sublanguages in the Ramadge-Wonham framework. We establish a general version of Zheng's hierarchical consistency by first achieving control consistency -preservation of control structures through tile aggregation mapping in a two-level hierarchy. For a refinement of hierarchical consistency with preservation of nonbtocking, the concept of observer is introduced via congruences on nondeterministic transition structures.

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I wish to thank firstly my supervisor Professor John Moore for his support and encour agement. I am specially grateful to Dr Kai Wong for his ideas, comments, many enjoyable discussions and his inspiration on the subject of this thesis. I also would like to thank Dr. Robert Mahony and Professor Iven Mareels for their ideas and comments on the areas in adap tive control. I am also grateful to Leonardo Kammer and Robert Orsi for their friendship and good advice on LaTeX and Matlab. With them, I feel more comfortable during my study. I wish to thank Professor Murray Wonham from the University of Toronto for the TCT software which is used for synthesising supervisors throughout this thesis. I also would like to thank Dr. Jayantha Katupitiya from University of New South Wales, my master degree supervisor, for his encouragement and good advice. I would like to acknowledge the financial support from ANU graduate school and CRAsys. I also would like to thank my family in Korea, especially my brother Sang-Tag Lee, for their spiritual support. I wish to thank my wife Eun-Joo Chong Lee for her persistent sup port and love. Finally, without smiles and endless implicit encouragement of my daughter, Nara Jee-Hyong, and my son, Joshua Min-Hyong, this thesis surely would not exist. Their understanding, support and especially patience are the most important stimuli during my study.

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Abstract. An abstract hierarchical control theory is developed lbr a class of timed discrete-event systems (TDES) within the discrete-event control architectural framework proposed earlier by the authors. For this development, a control theory for TDES is introduced in the spirit of a prior theory of Brandin. A notion of time control structures is introduced, and on its basis a general property of hierarchical consistency is achieved by establishing control consistency -namely preservation of time control structures through the aggregation mapping in a two-level hierarchy.