Clelland, Jeanne N.; Moseley, Christopher G.; Wilkens, George R. Geometry of optimal control for control-affine systems. (English) Zbl 1267.93036 SIGMA, Symmetry Integrability Geom. Methods Appl. 9, Paper 034, 31 p. (2013). Summary: 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 two states and one control and systems with three states and one 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. Cited in 2 Documents MSC: 93B27 Geometric methods 49K15 Optimality conditions for problems involving ordinary differential equations 53C17 Sub-Riemannian geometry 58A15 Exterior differential systems (Cartan theory) 53C10 \(G\)-structures Keywords:affine distributions; optimal control theory; Cartan’s method of equivalence; geodesic trajectories; Pontryagin’s maximum principle; local isometric invariants PDFBibTeX XMLCite \textit{J. N. Clelland} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 9, Paper 034, 31 p. (2013; Zbl 1267.93036) Full Text: DOI arXiv