  The scattering of waves in a complex medium is perturbed by polarizability
changes or motion of embedded targets. These perturbations could serve as
perfectly non-invasive guidestars for focusing on the targets. In this Letter,
we theoretically derive a fundamental difference between these two perturbation
types (the change of the scattering matrix is of rank one [two] for target
polarizability changes [motion]) and identify accordingly optimal strategies to
perfectly focus on the target in both cases. For target motion, at least two
displacements are necessary. Furthermore, for the case of dynamic complex media
additionally featuring parasitic perturbers, we establish a non-invasive scheme
to achieve optimal time-averaged power delivery to a perturbation-inducing
target. In all cases, no assumptions about the unitarity of the system's
scattering matrix or the size of the perturbation are necessary. We
experimentally demonstrate all results in the microwave regime using a strongly
sub-unitary lossy chaotic cavity as complex medium. Our experiments highlight
that the target's "structural scattering" is irrelevant [must be negligible] in
the case of target polarizability changes [motion]. We expect our results to
find applications in communications, cybersecurity, bioelectronics,
flow-cytometry and self-propelled nano-swimmers.
