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Smarandache Sequences: Explorations and Discoveries with a Computer Algebra System
Paulo D. F. Gouveia, Delfim F. M. Torres
We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.
On the Constancy of the Pontryagin Hamiltonian for Autonomous Problems
Delfim F. M. Torres
We provide a new, simpler, and more direct proof of the well known fact that for autonomous optimal control problems the Pontryagin extremals evolve on a level surface of the respe…
Quasi-Invariant Optimal Control Problems
Delfim F. M. Torres
We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryag…
A Proper Extension of Noether's Symmetry Theorem for Nonsmooth Extremals of the Calculus of Variations
Delfim F. M. Torres
For nonsmooth Euler-Lagrange extremals, Noether's conservation laws cease to be valid. We show that Emmy Noether's theorem of the calculus of variations is still valid in the wider…
Integrals of Motion for Discrete-Time Optimal Control Problems
Delfim F. M. Torres
We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be…
Gauge Symmetries and Noether Currents in Optimal Control
Delfim F. M. Torres
We extend the second Noether theorem to optimal control problems which are invariant under symmetries depending upon k arbitrary functions of the independent variable and their der…