Control parameterization technique is an effective method to solve optimal control problems. It works by approximating the function piece-wise constant (or linear) function. In this way, problems are approximated parameter selection problems, which can be regarded as finite-dimensional optimization where heights and switching times of taken decision variables. They solved using gradient-based m...

We extend the DuBois-Reymond necessary optimality condition and Noether’s symmetry theorem to the scale relativity theory setting. Both Lagrangian and Hamiltonian versions of Noether’s theorem are proved, covering problems of the calculus of variations with functionals defined on sets of non-differentiable functions, as well as more general non-differentiable problems of optimal control. As an ...