Abstract
We present some results on feed back stabilization of nonlinear beams and space craft with flexible appendages by use of controls applied to the boundary of flexible members. Semigroup theory and basic concepts of Lyapunov functions are used to prove stability, asymptotic stability, and exponential stability.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N. U. Ahmed and S. S. Lim, “Modeling and control of flexible space stations (slew maneuvers)”, Proceedings of the 3rd Annual Conference on Aerospace Computational Control (D.E. Bernard and G.K. Mann, Eds.), JPL, NASA Pub. 89–45, Vol. 2, pp. 900–914, 1989.
N. U. Ahmed and S. K. Biswas, “Mathematical modeling and control of large space structures with multiple appendages”, J. Math. Comput. Modeling Vol. 10, pp. 891–900, 1988.
N. U. Ahmed, “Stability and control of nonlinear flexible systems”, Dynamic Systems and Applications (submitted).
N. U. Ahmed, Elements of Finite Dimensional Systems and Control Theory Longman Scientific and Technical, UK, 1988.
S. K. Biswas and N.U. Ahmed, “Optimal control of large space structures governed by a coupled system of ordinary and partial differential equations”, J. Math. Control, Signals, and Systems Vol. 2, pp. 1–18, 1989.
G. Chen, S. G. Krantz, D. W. Ma and C. E. Wayne, “The Euler-Bernoulli beam equation with boundary energy dissipation”, in Operator Methods in Optimal Control Problems (Sung J. Lee, Ed.), Marcel Dekker lecture notes, Vol. 108, pp. 67–96, 1987.
I. Lasiecka, “Stabilization of hyperbolic and parabolic systems with nonlinearly perturbed boundary conditions”, J. Duff Equations Vol. 75, pp. 53–87, 1988.
P. Li and N. U. Ahmed, “On exponential stability of infinite dimensional systems with bounded or unbounded perturbations”, Applicable Analysis Vol. 30, pp. 175–187, 1988.
P. Li, N. U. Ahmed and S. S. Lim, “Robust boundary control of flexible structures governed by hybrid dynamics”, Canadian Conference on Electrical and Computer Engineering pp. 18.3.1–18.3.4., 1990.
J. M. Skowronski, H. Flashner and R. S. Gutalu (Eds.), Mechanics and Control Proceedings of the 3rd Workshop on Control Mechanics, Springer-Verlag, Berlin, Vol. 151, 1991.
S. K. Srinivasan and R. Vasudevan, Introduction to Random Differential Equations and Their Applications Elsevier, New York, 1971.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ahmed, N.U., Skowronski, J.M. (1994). Boundary Stabilization of Nonlinear Flexible Systems. In: Guttalu, R.S. (eds) Mechanics and Control. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2425-0_18
Download citation
DOI: https://doi.org/10.1007/978-1-4615-2425-0_18
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6029-2
Online ISBN: 978-1-4615-2425-0
eBook Packages: Springer Book Archive