  In this paper, we derive a version of the Pontryagin maximum principle for
general finite-dimensional nonlinear optimal sampled-data control problems. Our
framework is actually much more general, and we treat optimal control problems
for which the state variable evolves on a given time scale (arbitrary non-empty
closed subset of R), and the control variable evolves on a smaller time scale.
Sampled-data systems are then a particular case. Our proof is based on the
construction of appropriate needle-like variations and on the Ekeland
variational principle.
