| 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.
|
| Files |
| Filename |
Size |
Approximate Download Time
(Hours:Minutes:Seconds)
|
| 28.8 Modem |
56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
Higher-speed Access |
| |
main.pdf |
482.57 Kb |
00:02:14 |
00:01:08 |
00:01:00 |
00:00:30 |
00:00:02 |
|
