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Full-Text Articles in Algebraic Geometry
Geometry Of Optimal Control For Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
Geometry Of Optimal Control For Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
University Faculty Publications and Creative Works
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.
Geometry Of Optimal Control For Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
Geometry Of Optimal Control For Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
University Faculty Publications and Creative Works
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.
Geometry Of Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
Geometry Of Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
University Faculty Publications and Creative Works
Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X) = n, rank(F) = n - 1, and when dim(X) = 3, rank(F) = 1. Unlike linear distributions, which are characterized by integer- valued invariants - namely, the rank and growth vector - when dim(X) ≤ 4, we find local invariants depending on arbitrary functions even for rank 1 point-affine distributions on manifolds …
Geometry Of Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
Geometry Of Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
University Faculty Publications and Creative Works
Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X) = n, rank(F) = n - 1, and when dim(X) = 3, rank(F) = 1. Unlike linear distributions, which are characterized by integer- valued invariants - namely, the rank and growth vector - when dim(X) ≤ 4, we find local invariants depending on arbitrary functions even for rank 1 point-affine distributions on manifolds …