Left-invariant optimal control problems on Lie groups that are integrable by elliptic functions

Left-invariant optimal control problems on Lie groups are an important class of with a large symmetry group. They theoretically interesting because they can often be investigated in full and general laws studied by using these model problems. In particular, nilpotent provide fundamental approximation to Also, left-invariant arise applications such as classical quantum mechanics, geometry, robotics, visual perception models, image processing. The aim this paper is present survey the main concepts, methods, results pertaining that integrated elliptic functions. focus describing extremal trajectories their optimality, cut time locus, synthesis. Bibliography: 162 titles.