Work

Geometry of Optimal Control for Control-Affine Systems

Year: 2013

Type: article

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.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2013.034

Author: Jeanne N. Clelland

Institution: University of Colorado Boulder

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: Isometric Embedding and Other Problems in Geometry and Differential Equations, Topics in the Geometry of Differential Equations