  We present an extension of some results of higher order calculus of
variations and optimal control to generalized functions. The framework is the
category of generalized smooth functions, which includes Schwartz
distributions, while sharing many nonlinear properties with ordinary smooth
functions. We prove the higher order Euler-Lagrange equations, the D'Alembert
principle in differential form, the du Bois-Reymond optimality condition and
the Noether's theorem. We start the theory of optimal control proving a weak
form of the Pontryagin maximum principle and the Noether's theorem for optimal
control. We close with a study of a singularly variable length pendulum,
oscillations damped by two media and the Pais-Uhlenbeck oscillator with
singular frequencies.
