Title page for ETD etd-03232008-175232


Type of Document Master's Thesis
Author Boquet, Grant Michael
Author's Email Address gboquet@vt.edu
URN etd-03232008-175232
Title Multidimensional Behavioral Complexes
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Ball, Joseph A. Committee Chair
Haskell, Peter E. Committee Member
Linnell, Peter A. Committee Member
Keywords
  • multidimensional systems theory
  • homology
  • Behavioral systems theory
Date of Defense 2008-03-19
Availability unrestricted
Abstract
In a preprint by J. Wood, V. Lomadze, and E. Rogers, chains and boundary maps were defined for 2-D discrete behavioral systems. The corresponding homology groups were studied and tied to trajectory properties. Indeed, the homology groups encapsulated the concepts of autonomy, controllability, and signal restriction.

We shall present an extension of their work to n-D discrete behavioral systems. In particular, we shall streamline the construction of the chain groups, the boundary maps between chains, and the study of the resultant homology groups. While constructing this machinery, we shall point out intrinsic flaws in their approach that make extension of their results less systematic. Finishing remarks shall be made on using the homology groups to determine system properties and potentially classify forms of controllability.

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