On the equivalence of higher order variational problems and optimal control problems

We consider the equivalence of higher order variational problems and optimal control problems. Our work is motivated by a series of problems, such as the optimal control of mechanical systems, representation and simulation of stochastic processes, and interpolation problems applied to trajectory generation for control systems, such as aircraft. Generating a Hamiltonian formulation of higher order variational problems is classical and goes back to Ostrogradsky. However, even in the classical variational problem, the relation with optimal control problems has not been studied extensively. Here, we generalize earlier work by the authors to this case.