Abstract
In the middle 1980’s, the space shuttle program gave rise to an array of interesting control problems. Among the prototype models considered by NASA was the “Spacecraft Control Laboratory Experiment” (SCOLE) [2]. In this model, a large rigid body, the space shuttle, is joined to a small rigid body, the antenna, via a long flexible mast. The motions of the two rigid bodies are governed by ordinary differential equations, while the motion of the mast is governed by the equations of a vibrating beam with appropriate boundary conditions at the two ends originating from forces and torques exerted by the attached rigid bodies.
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
Avalos, G. and Lasiecka, I. (1995), “The strong stability of a semigroup arising from a coupled hyperbolic/parabolic systems,” University of Minnesota, IMA Preprint #1347.
Balakrishnan, A.V. and Taylor, L. (1986), The SCOLE Design Challenge,3rd annual NASA-SCOLE Workshop.
Beale, J.T. (1976), “Spectral properties of an acoustic boundary condition,” Indiana Univ. Math. J., Vol. 25, No. 9, 895–917.
Chen, G., Delfour, M., Krall, A. and Payre, G. (1987), “Modelling stabilization and control of serially connected beams,” SIAM J. Control Optim., Vol. 25, 526–546.
Hansen, S. and Zuazua, E. (1993), “Exact controllability and stabilization of a vibrating string with an interior point,” IMA Preprint #1140.
Littman, W. and Liu, B., “On the spectral properties and stabilization of acoustic flow,” Siam J. Appl. Math., IMA Preprint #1436, 1996,to appear.
Littman, W. and Liu, B. (1996), “The regularity and singularity of solutions of certain elliptic problems on polygonal domains,” IMA #1412.
Littman, W. and Markus, L. (1988), “Some recent results on control and stabilization of flexible structures,” A. V. Balakrishnan and J.P. Zolesio, eds., Optimization Software Inc., 151–161.
Liu, B., Stabilization of a Membrane with Strings on General Polygonal Domains, manuscript.
Markus, L. (1993), “Concepts and problems for hybrid control systems,” in Proceedings of International Meeting on Ordinary Differential Equations and Their Applications, Florence, 99–126.
Micu, S.D. and Zuazua, E. (1994), “Propriétés qualitatives d’un modèle hybride bi-dimensionnel intervenant dans le contrôle du bruit,” C.R. Acad. Sci. Paris Ser. I, Math., Vol. 319, No. 12, 1263–1268.
Rao, B. (1995), “Stabilization d’une equation de plaque par contrôle frontière dynamique,” 321, Ser., 1449–1454.
Taylor, S.W. (1995), “Exact boundary control of a beam and mass system,” in Progress in System and Control Theory, Computation and Control VI, Bowers and Lund, eds., Birkhäuser, Basel.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Littman, W., Liu, B. (1998). Remarks on Hybrid Systems. In: Optimal Control. Applied Optimization, vol 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6095-8_16
Download citation
DOI: https://doi.org/10.1007/978-1-4757-6095-8_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4796-3
Online ISBN: 978-1-4757-6095-8
eBook Packages: Springer Book Archive