Uniqueness of solutions for control systems with degenerate Lagrangians

We outline a method for dealing with controlled mechanical systems with degenerate Lagrangians, or singular optimal control problems with degenerate cost functions. We show how consistent equations of motion can be obtained despite the-implicit-constraint of degeneracy, and state conditions on which the system exhibits unique solutions (on a reduced phase space). This method is adopted from results in classical mechanics, viz. the Gotay-Nester-Hinds algorithm for the resolution of constraints in presymplectic systems. We illustrate with an example from singular linear optimal control theory