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Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping

Bloch, Anthony M. and Chang, Dong Eui and Leonard, Naomi Ehrich and Marsden, Jerrold E. (2001) Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping. IEEE Transactions on Automatic Control, 46 (10). pp. 1556-1571. ISSN 0018-9286. doi:10.1109/9.956051.

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For pt.I, see ibid., vol.45, p.2253-70 (2000). We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline.

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Additional Information:© 2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” Manuscript received August 16, 2000; revised February 23, 2001 and March 9, 2001. Recommended by Associate Editor K. Gu. This work was supported in part by Grants from the National Science Foundation, the Air Force Office of Scientific Research, and ONR.
Subject Keywords:Lyapunov methods, mechanical systems, nonlinear control, stabilization, tracking
Issue or Number:10
Record Number:CaltechAUTHORS:BLOieeetac01
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:533
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Deposited On:14 Jul 2005
Last Modified:08 Nov 2021 19:03

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