In many applications of vibratory energy harvesting, the external disturbance are most appropriately modeled as
broadband stochastic processes. Optimization of power generation from such disturbances is a feedback control
problem, and solvable via a LQG control theory. However, attainment of this performance requires the power
conversion system which interfaces the transducers with energy storage to be capable of bi-directional power flow,
and there are many applications where this is infeasible. One of the most common approaches to power extraction
with one-directional power flow constraints is to control the power conversion system to create a purely resistive
input impedance, and then to optimize this effective resistance for maximal absorption. This paper examines
the optimization of broadband energy harvesting controllers, subject to the constraint of one-directional power
flow. We show that as with the unconstrained control problem, it can be framed as a "Quadratic-Gaussian"
stochastic optimal control problem, although its solution is nonlinear and does not have a closed-form. This paper
discusses the mathematics for obtaining the optimal power extraction controller for this problem, which involves
the stationary solution to an associated Bellman-type partial differential equation. Because the numerical solution
to this PDE is computationally prohibitive for harvester dynamics of even moderate complexity, a sub-optimal
control design technique is presented, which is comparatively simple to compute and which exhibits analyticallycomputable lower bounds on generated power Examples focus a nondimensionalized, ideal, base-excited SDOF resonator with electromagnetic transduction.