Controllability for Systems with Slowly Varying Parameters

Fritz Colonius; Roberta Fabbri

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 9, page 207-216
  • ISSN: 1292-8119

Abstract

top
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.

How to cite

top

Colonius, Fritz, and Fabbri, Roberta. "Controllability for Systems with Slowly Varying Parameters." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 207-216. <http://eudml.org/doc/90692>.

@article{Colonius2010,
abstract = { 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. },
author = {Colonius, Fritz, Fabbri, Roberta},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Control sets; control bundles; singular perturbations.; control sets; singular perturbations},
language = {eng},
month = {3},
pages = {207-216},
publisher = {EDP Sciences},
title = {Controllability for Systems with Slowly Varying Parameters},
url = {http://eudml.org/doc/90692},
volume = {9},
year = {2010},
}

TY - JOUR
AU - Colonius, Fritz
AU - Fabbri, Roberta
TI - Controllability for Systems with Slowly Varying Parameters
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 9
SP - 207
EP - 216
AB - 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.
LA - eng
KW - Control sets; control bundles; singular perturbations.; control sets; singular perturbations
UR - http://eudml.org/doc/90692
ER -

References

top
  1. Z. Artstein, Stability in the presence of singular perturbations. Nonlinear Anal. TMA34 (1998) 817-827.  Zbl0948.34029
  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.  Zbl0908.49002
  3. I.U. Bronstein and A.Ya. Kopanskii, Smooth Invariant Manifolds and Normal Forms. World Scientific (1994).  
  4. F. Colonius and W. Kliemann, The Dynamics of Control. Birkhäuser (2000).  Zbl1020.93500
  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.  Zbl0999.93028
  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. TMA28 (1997) 1855-1865.  
  8. G. Grammel and P. Shi, On the asymptotics of the Lyapunov spectrum under singular perturbations. IEEE Trans. Automat. Control45 (2000) 565-568.  Zbl0978.93043
  9. S.M. Grünvogel, Lyapunov Spectrum and Control Sets, Dissertation Universität Augsburg. Augsburger Mathematische Schriften No. 34, Wißner Verlag, Augsburg (2000).  
  10. S.M. Grünvogel, Lyapunov exponents and control sets near singular points. J. Differential Equations (to appear).  
  11. H.K. Khalil, Nonlinear Systems. Prentice Hall (1996).  
  12. P.V. Kokotovic, H.K. Khalil and J. O'Reilly, Singular Perturbation Methods in Control: Analysis and Design. Academic Press (1986).  
  13. M.S. Soliman and J.M.T. Thompson, Stochastic penetration of smooth and fractal basin boundaries under noise excitation. Dynam. Stability Systems5 (1990) 281-298.  Zbl0726.70020
  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).  Zbl1120.93007
  16. A. Vigodner, Limits of singularly perturbed control problems with statistical dynamics of fast motions. SIAM J. Control Optim.35 (1997) 1-28.  Zbl0882.49001

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.