IFAC-PapersOnLine | 2021
Elliptic Optimal Control and Symmetric Sub-Riemannian Spaces
Abstract
Abstract In this paper we study the integrability properties of Lie-Poisson adjoint systems associated to four-dimensional sub-Riemannian Lie groups with invariant quasi-contact distributions. We show an equivalence between the facts that this system admits three quadratic functionally independent first integrals, the optimal controls are elliptic functions, and the sub-Riemannian space is symmetric.