  H$_2^+$ is an ideal candidate for a detailed study of strong field coherent
control strategies inspired by basic mechanisms referring to some specific
photodissociation resonances. Two of them are considered in this work, namely:
Zero-width resonances (ZWR) on one hand, and coalescing pairs of resonances at
exceptional points (EP) on the other hand. An adiabatic transport theory based
on Floquet Hamiltonian formalism is developed within the challenging context of
multiphoton dynamics involving nuclear continua. It is shown that a rigorous
treatment is only possible for ZWRs, whereas adiabatic transport mediated by
EPs is subjected to restrictions. Numerical maps of resonance widths and
non-adiabatic couplings in the laser parameter plane help in optimally shaping
control pulses. Full time-dependent wavepacket dynamics shows the possibility
of selective, robust filtration and vibrational population transfers, within
experimental feasibility criteria.
