Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales

TL;DR

This paper applies Leitmann's direct method to solve specific calculus of variations problems on arbitrary time scales, unifying discrete, quantum, and classical cases with explicit solutions.

Contribution

It extends Leitmann's direct method to the calculus of variations on time scales, providing explicit solutions for certain optimal control problems.

Findings

Explicit solutions for variational problems on arbitrary time scales.

Unified approach encompassing discrete, quantum, and classical cases.

Demonstration of Leitmann's method effectiveness in this context.

Abstract

The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. This includes the discrete-time, the quantum, and the continuous/classical calculus of variations as particular cases. In this note we follow Leitmann's direct method to give explicit solutions for some concrete optimal control problems on an arbitrary time scale.