  Ease of miniaturization and minimal maintenance are among the advantages for
replacing conventional batteries with vibratory energy harvesters in a wide of
range of disciplines and applications, from wireless communication sensors to
medical implants. However, the current harvesters do not extract energy from
the ambient vibrations in a very efficient and robust fashion, and hence, there
need to be more optimal harvesting approaches. In this paper, we introduce a
generic architecture for vibration energy harvesting and delineate the key
challenges in the field. Then, we formulate an optimal control problem to
maximize the harvested energy. Though possessing similar structure to that of
the standard LQG problem, this optimal control problem is inherently different
from the LQG problem and poses theoretical challenges to control community. As
the first step, we simplify it to a tractable problem of optimizing control
gains for a linear system subjected to Gaussian white noise excitation, and
show that this optimal problem has non-trivial optimal solutions in both time
and frequency domains.
