On the Noether Invariance Principle for Constrained Optimal Control Problems

Noether’s invariance principle is one of the most helpful and fundamental results of physics. It describes the universal fact that “invariance with respect to some family of parameter transformations gives rise to the existence of certain conserved quantities.” Such relation is used to explain everything from the fusion of hydrogen to the motion of planets orbiting the sun [6]. For a modern account of Noether’s invariance principle, in the context of the calculus of variations, we refer the reader to [1, 10]. Extensions for the unconstrained problems of optimal control are available in [8, 9]. Here we generalize the previous results