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Controllability for Systems with Slowly Varying Parameters

Published online by Cambridge University Press:  15 September 2003

Fritz Colonius  and
Roberta Fabbri
Fritz Colonius
Affiliation:
Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany; [email protected].
Roberta Fabbri
Affiliation:
Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Via Santa Marta 3, 50139 Firenze, Italy; [email protected].
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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.

Keywords

Control setscontrol bundlessingular perturbations.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 9 , January 2003 , pp. 207 - 216
Copyright
© EDP Sciences, SMAI, 2003

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References

Artstein, Z., Stability in the presence of singular perturbations. Nonlinear Anal. TMA 34 (1998) 817-827. CrossRef
Artstein, Z. and Gaitsgory, V., Tracking fast trajectories along a slow dynamics: A singular perturbations approach. SIAM J. Control Optim. 35 (1997) 1487-1507. CrossRef
I.U. Bronstein and A.Ya. Kopanskii, Smooth Invariant Manifolds and Normal Forms. World Scientific (1994).
F. Colonius and W. Kliemann, The Dynamics of Control. Birkhäuser (2000).
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.
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).
Grammel, G., Averaging of singularly perturbed systems. Nonlinear Anal. TMA 28 (1997) 1855-1865. CrossRef
Grammel, G. and Shi, P., On the asymptotics of the Lyapunov spectrum under singular perturbations. IEEE Trans. Automat. Control 45 (2000) 565-568. CrossRef
S.M. Grünvogel, Lyapunov Spectrum and Control Sets, Dissertation Universität Augsburg. Augsburger Mathematische Schriften No. 34, Wißner Verlag, Augsburg (2000).
S.M. Grünvogel, Lyapunov exponents and control sets near singular points. J. Differential Equations (to appear).
H.K. Khalil, Nonlinear Systems. Prentice Hall (1996).
P.V. Kokotovic, H.K. Khalil and J. O'Reilly, Singular Perturbation Methods in Control: Analysis and Design. Academic Press (1986).
Soliman, M.S. and Thompson, J.M.T., Stochastic penetration of smooth and fractal basin boundaries under noise excitation. Dynam. Stability Systems 5 (1990) 281-298. CrossRef
D. Szolnoki, Algorithms for Reachability Problems, Dissertation. Institut für Mathematik, Universität Augsburg, Augsburg (2001).
D. Szolnoki, Set oriented methods for computing reachable sets and control sets. Discrete Contin. Dynam. Systems Ser. B (submitted).
Vigodner, A., Limits of singularly perturbed control problems with statistical dynamics of fast motions. SIAM J. Control Optim. 35 (1997) 1-28. CrossRef