Calculus of variations and optimal control for generalized functions

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