Continuous and discrete embedded optimal control problems and their application to the analysis of Clebsch optimal control problems and mechanical systems (Q1951365)

This paper is concerned with the theory of embedded optimal control problems. Among others, the authors show how the extremal generating equations for an embedded optimal control problem project to the extremal generating the equations for an associated optimal control problem and show how to construct a Clebsch optimal control for which an associated optimal control problem is equivalent to a given variational problem. They also obtain results for discrete embedded optimal control problems, that are analogous to the continuous results. Applications are given to mechanical systems on matrix Lie groups and mechanical systems on \(n\)-spheres.