|
Controllability properties of nonlinear behaviors
Author(s):
Fritz
Colonius;
Wolfgang
Kliemann
Journal:
Trans. Amer. Math. Soc.
360
(2008),
5667-5682.
MSC (2000):
Primary 37N35, 93B05
Posted:
June 19, 2008
MathSciNet review:
2425687
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
This paper proposes a topological framework for the analysis of the time shift on behaviors. It is shown that controllability is not a property of the time shift, while chain controllability is. This also leads to a global decomposition of behaviors.
References:
-
- 1.
- M. V. BEBUTOV, Dynamical systems in the space of continuous functions, Dokl. Akad. Nauk SSSR, 27 (1940), pp. 904-906.
In Russian. - 2.
- F. COLONIUS AND W. KLIEMANN, Some aspects of control systems as dynamical systems, J. Dyn. Diff. Equations, 5 (1993), pp. 469-494. MR 1235039 (94g:93063)
- 3.
-
-, The Dynamics of Control, Birkhäuser, Boston, 2000. - 4.
-
-, Behaviors and controllability, in Electronic Proceedings of the 16th Conference on Mathematical Theory of Networks and Systems (MTNS), July 5-9, 2004, Leuven (Belgium), 2004. - 5.
- F. COLONIUS AND M. SPADINI, Uniqueness of local control sets, J. Dynamical and Control Systems, 9 (2003), pp. 513-530. MR 2001957 (2004f:93010)
- 6.
- R. EASTON, Geometric Methods for Discrete Dynamical Systems, Oxford University Press, 1998. MR 1616726 (2000e:37002)
- 7.
- T. GAYER, Control sets and their boundaries under parameter variation, J. Diff. Equations, 201 (2004), pp. 177-200. MR 2057543 (2005g:93063)
- 8.
- M. GOLUBITSKY AND D. SCHAEFFER, Singularities and Groups in Bifurcation Theory, Springer-Verlag, 1985. MR 771477 (86e:58014)
- 9.
- S. PILYUGIN, The Space of Dynamical Systems with the
 -Topology, Springer-Verlag, 1994. MR 1329732 (96g:58049) - 10.
- J. W. POLDERMAN AND J. C. WILLEMS, Introduction to Mathematical Systems Theory. A Behavioral Approach, Springer-Verlag, 1997. MR 1480665 (99f:93001)
- 11.
- A. B. POORE, A model equation arising from chemical reactor theory, Arch. Rational Mech. Anal., 52 (1974), pp. 358-388. MR 0338508 (49:3272)
- 12.
- C. ROBINSON, Dynamical Systems. Stability, Symbolic Dynamics, and Chaos, CRC Press Inc., 1995. MR 1396532 (97e:58064)
- 13.
- D. SALAMON AND E. ZEHNDER, Flows on vector bundles and hyperbolic sets, Trans. Amer. Math. Soc., 306 (1988), pp. 623-649. MR 933310 (89f:58112)
- 14.
- N. SCHERBINA, Continuity of one-parameter families of sets, Dokl. Ak. Nauk SSSR, 234 (1977), pp. 327-329.
In Russian. MR 0440500 (55:13375) - 15.
- G. R. SELL, Topological Dynamics and Ordinary Differential Equations, Van Nostrand Reinhold, London, 1971. MR 0442908 (56:1283)
- 16.
- D. SZOLNOKI, Set oriented methods for computing reachable sets and control sets, Discrete and Continuous Dynamical Systems-Series B, 3 (2003), pp. 361-382. MR 1974152 (2004a:93007)
- 17.
- J. C. WILLEMS, Models for dynamics, in Dynamics Reported, Vol. 2, U. Kirchgraber and H. Walther, eds., Teubner, 1989, pp. 171-269. MR 1000978 (90g:58121)
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2000):
37N35, 93B05
Retrieve articles in all Journals with
MSC (2000):
37N35, 93B05
Additional Information:
Fritz
Colonius
Affiliation:
Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany
Email:
fritz.colonius@math.uni-augsburg.de
Wolfgang
Kliemann
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email:
kliemann@iastate.edu
DOI:
10.1090/S0002-9947-08-04612-6
PII:
S 0002-9947(08)04612-6
Keywords:
Nonlinear control systems,
controllability,
behaviors
Received by editor(s):
March 21, 2005
Posted:
June 19, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
