| Title:
|
Reachability and observability of linear systems over max-plus (English) |
| Author:
|
Gazarik, Michael J. |
| Author:
|
Kamen, Edward W. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
[2]-12 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper discusses the properties of reachability and observability for linear systems over the max-plus algebra. Working in the event-domain, the concept of asticity is used to develop conditions for weak reachability and weak observability. In the reachability problem, residuation is used to determine if a state is reachable and to generate the required control sequence to reach it. In the observability problem, residuation is used to estimate the state. Finally, as in the continuous-variable case, a duality is shown to exist between the two properties. (English) |
| Keyword:
|
reachability |
| Keyword:
|
observability |
| Keyword:
|
linear system |
| Keyword:
|
max-plus algebra |
| MSC:
|
15A80 |
| MSC:
|
93B03 |
| MSC:
|
93B05 |
| MSC:
|
93B07 |
| MSC:
|
93B25 |
| MSC:
|
93C65 |
| MSC:
|
93C83 |
| idZBL:
|
Zbl 1274.93037 |
| idMR:
|
MR1705526 |
| . |
| Date available:
|
2009-09-24T19:22:47Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135263 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Cohen G., Moller P., Quadrat J., Viot M.: Algebraic tools for the performance evaluation of discrete event systems.Proc. IEEE 77 (1989), 39–58 |
| Reference:
|
[4] Cuninghame–Green R. A.: Minimax Algebra.Springer Verlag, New York 1979 Zbl 0739.90073, MR 0580321 |
| Reference:
|
[5] Doustmohammadi A., Kamen E.: Direct generation of event–timing equations for generalized flow shop systems.In: Proceedings of the SPIE Photonics East 1995 Symposium, Philadelphia 1995, pp. 50–62 |
| Reference:
|
[6] Gazarik M.: Monitoring and Control of Manufacturing Systems Based on the Max–plus Formulation.Ph.D. Thesis, Georgia Institute of Technology, Atlanta 1997 |
| Reference:
|
[7] Gazarik M., Kamen E.: Reachability and observability of linear systems over max–plus.In: 5th IEEE Mediterranean Conference on Control and Systems, Paphos 1997 MR 1705526 |
| Reference:
|
[8] Kamen E. W.: An Equation–based approach to the control of discrete event systems with applications to manufacturing.In: International Conference on Control Theory and Its Applications, Jerusalem 1993 |
| Reference:
|
[9] Olsder G., Roos C.: Cramer and Cayley–Hamilton in the max algebra.Linear Algebra Appl. 101 (1988), 87–108 Zbl 0659.15012, MR 0941298 |
| Reference:
|
[10] Prou J.-M., Wagneur E.: Controllability in the Max-algebra.In: 5th IEEE Mediterranean Conference on Control and Systems, Paphos 1997, revised version: Kybernetika 35 (1999), 13–24 MR 1705527 |
| . |
