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Control and stabilization of systems with homoclinic orbits

Bloch, A. M. and Marsden, J. E. (1989) Control and stabilization of systems with homoclinic orbits. In: Proceedings of the 28th Conference on Decision and Control Tampa, Florida, 13-15 December 1989. Vol.3. IEEE , Piscataway, NJ, pp. 2238-2242.

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In this paper we consider the control of two physical systems, the near wall region of a turbulent boundary layer and the rigid body, using techniques from the theory of nonlinear dynamical systems. Both these systems have saddle points linked by heteroclinic orbits. In the fluid system we show how the structure of the phase space can be used to keep the system near an (unstable) saddle. For the rigid body system we discuss passage along the orbit as a possible control manouver, and show how the Energy-Casimir method can be used to analyze stabilization of the system about the saddles.

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Additional Information:© Copyright 1989 IEEE. Reprinted with permission. Supported in part by NSF Grant DMS-87-01576 and AFOSR Grant AFOSR-ISSA-87-0077 and by the USARO through MSI at Cornell University. Supported in part by DOE Contract DE-AT03-88ER-12097 and by MSI at Cornell University and by AFOSR Contract No. 88-NA-321.
Subject Keywords:boundary layer turbulence; nonlinear control systems; phase space methods; stability; energy-Casimir method; homoclinic orbits; near wall region; nonlinear dynamical systems; nonlinear systems; phase space structure; rigid body; saddle points; turbulent boundary layer
Record Number:CaltechAUTHORS:BLOieeecdc89
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9592
Deposited On:13 Feb 2008
Last Modified:08 Nov 2021 21:00

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