| Title:
|
A study on global stabilization of periodic orbits in discrete-time chaotic systems by using symbolic dynamics (English) |
| Author:
|
Suzuki, Masayasu |
| Author:
|
Sakamoto, Noboru |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
4-19 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this report, a control method for the stabilization of periodic orbits for a class of one- and two-dimensional discrete-time systems that are topologically conjugate to symbolic dynamical systems is proposed and applied to a population model in an ecosystem and the Smale horseshoe map. A periodic orbit is assigned as a target by giving a sequence in which symbols have periodicity. As a consequence, it is shown that any periodic orbits can be globally stabilized by using arbitrarily small control inputs. This work is a new attempt to systematically design a control system based on symbolic dynamics in the sense that one estimates the magnitude of control inputs and analyzes the Lyapunov stability. (English) |
| Keyword:
|
symbolic dynamics |
| Keyword:
|
chaos control |
| Keyword:
|
global stability |
| MSC:
|
37B10 |
| MSC:
|
37N35 |
| MSC:
|
74H65 |
| MSC:
|
93D15 |
| idZBL:
|
Zbl 06433829 |
| idMR:
|
MR3333830 |
| DOI:
|
10.14736/kyb-2015-1-0004 |
| . |
| Date available:
|
2015-03-23T18:43:23Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144199 |
| . |
| Reference:
|
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| Reference:
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