Controllability for systems with slowly varying parameters
ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 207-216.

For systems with slowly varying parameters the controllability behavior is studied and the relation to the control sets for the systems with frozen parameters is clarified.

DOI : 10.1051/cocv:2003010
Classification : 93B05, 93C70
Mots-clés : control sets, control bundles, singular perturbations 
@article{COCV_2003__9__207_0,
     author = {Colonius, Fritz and Fabbri, Roberta},
     title = {Controllability for systems with slowly varying parameters},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {207--216},
     publisher = {EDP-Sciences},
     volume = {9},
     year = {2003},
     doi = {10.1051/cocv:2003010},
     mrnumber = {1957099},
     zbl = {1063.93006},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv:2003010/}
}
TY  - JOUR
AU  - Colonius, Fritz
AU  - Fabbri, Roberta
TI  - Controllability for systems with slowly varying parameters
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2003
SP  - 207
EP  - 216
VL  - 9
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/cocv:2003010/
DO  - 10.1051/cocv:2003010
LA  - en
ID  - COCV_2003__9__207_0
ER  - 
%0 Journal Article
%A Colonius, Fritz
%A Fabbri, Roberta
%T Controllability for systems with slowly varying parameters
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2003
%P 207-216
%V 9
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/cocv:2003010/
%R 10.1051/cocv:2003010
%G en
%F COCV_2003__9__207_0
Colonius, Fritz; Fabbri, Roberta. Controllability for systems with slowly varying parameters. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 207-216. doi : 10.1051/cocv:2003010. http://archive.numdam.org/articles/10.1051/cocv:2003010/

[1] Z. Artstein, Stability in the presence of singular perturbations. Nonlinear Anal. TMA 34 (1998) 817-827. | MR | Zbl

[2] Z. Artstein and V. Gaitsgory, Tracking fast trajectories along a slow dynamics: A singular perturbations approach. SIAM J. Control Optim. 35 (1997) 1487-1507. | MR | Zbl

[3] I.U. Bronstein and A.Ya. Kopanskii, Smooth Invariant Manifolds and Normal Forms. World Scientific (1994). | MR | Zbl

[4] F. Colonius and W. Kliemann, The Dynamics of Control. Birkhäuser (2000). | MR | Zbl

[5] F. Colonius and W. Kliemann, On dynamic bifurcations in control systems, in Proc. IFAC Symposium on Nonlinear Control Systems (NOLCOS '01), 4-6 July 2001. St. Petersburg, Russia (2001) 140-143.

[6] J. Fischer, R. Guder and E. Kreuzer, Analyzing Perturbed Nonlinear Dynamical Systems, in Proc. 9th German-Japanese Seminar “Nonlinear Problems in Dynamical Systems”. Straelen, Germany (to appear).

[7] G. Grammel, Averaging of singularly perturbed systems. Nonlinear Anal. TMA 28 (1997) 1855-1865. | MR | Zbl

[8] G. Grammel and P. Shi, On the asymptotics of the Lyapunov spectrum under singular perturbations. IEEE Trans. Automat. Control 45 (2000) 565-568. | MR | Zbl

[9] S.M. Grünvogel, Lyapunov Spectrum and Control Sets, Dissertation Universität Augsburg. Augsburger Mathematische Schriften No. 34, Wißner Verlag, Augsburg (2000). | MR | Zbl

[10] S.M. Grünvogel, Lyapunov exponents and control sets near singular points. J. Differential Equations (to appear). | MR | Zbl

[11] H.K. Khalil, Nonlinear Systems. Prentice Hall (1996). | Zbl

[12] P.V. Kokotovic, H.K. Khalil and J. O'Reilly, Singular Perturbation Methods in Control: Analysis and Design. Academic Press (1986). | Zbl

[13] M.S. Soliman and J.M.T. Thompson, Stochastic penetration of smooth and fractal basin boundaries under noise excitation. Dynam. Stability Systems 5 (1990) 281-298. | MR | Zbl

[14] D. Szolnoki, Algorithms for Reachability Problems, Dissertation. Institut für Mathematik, Universität Augsburg, Augsburg (2001).

[15] D. Szolnoki, Set oriented methods for computing reachable sets and control sets. Discrete Contin. Dynam. Systems Ser. B (submitted). | MR | Zbl

[16] A. Vigodner, Limits of singularly perturbed control problems with statistical dynamics of fast motions. SIAM J. Control Optim. 35 (1997) 1-28. | MR | Zbl

Cité par Sources :