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arXiv · 1206.1101

Geometry of Optimal Control for Control-Affine Systems

Jeanne N. Clelland·Christopher G. Moseley·George R. Wilkens
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Abstract

Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied.

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Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens. 2013-04-17. Geometry of Optimal Control for Control-Affine Systems. https://doi.org/10.3842/sigma.2013.034

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