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Optimal Control of Affine Connection Control Systems: A Variational Approach
Abstract In this paper we investigate the optimal c …
In this paper we investigate the optimal control of affine connection control systems. The formalism of the affine connection can be used to describe geometrically the dynamics of me chanical systems, including those with nonholonomic constraints. In the standard variational approach to such problems, one converts an n dimensional second order system into a 2n dimensional first order system, and uses these equations as constraints on the optimization. An alternative approach, which we develop in this paper, is to include the system dynamics as second order constraints of the optimization, and optimize relative to variations in the configuration space. Using the affine connection, its associated tensors, and the notion of covariant differentiation, we show how variations in the configuration space induce variations in the tangent space. In this setting, we derive second order equations have a geometric formulation parallel to that of the system dynamics. They also specialize to results found in the literature.
ialize to results found in the literature.  +
Authors Alex Fax and Richard Murray  +
ID 2000b  +
Source 2000 Conference on Decision and Control  +
Tag fm00-cdc  +
Title Optimal Control of Affine Connection Control Systems: A Variational Approach +
Type Conference Submission  +
Categories Papers
Modification date
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15 May 2016 06:19:29  +
URL
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http://www.cds.caltech.edu/~murray/preprints/fm00b-cdc.pdf  +
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Optimal Control of Affine Connection Control Systems: A Variational Approach + Title
 

 

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