Abstract: Energy harvesters are devices that have the capability to convert ambient energy available in their environments (e.g., mechanical vibrations, waves) into electricity. This talk will focus on applying optimal control techniques to energy harvesting systems, where the objective of these exogenously excited systems is to maximize the average generated power subject to constraints on their onboard energy storage. We restrict our attention to linear, discrete-time systems in the context of full-information open-loop control, in which it can be shown that the optimization problem is in general nonconvex because of the energy storage constraints. For this problem, we illustrate a technique to determine a lower bound on the optimal performance by transformation to a (convex) dual optimization, which may be solved uniquely and efficiently. We illustrate that if a certain easy-to-check condition holds for the obtained dual optimum, then there is no duality gap, and consequently the dual and primal optima are coincident. In this situation, it follows that this duality technique can be used as a convex means of solving the optimal control problem exactly. We illustrate this technique at a small scale via a piezoelectric energy harvester and at a large scale via a wave energy converter for a range of energy storage constraints. The talk will conclude with a discussion about extending these techniques to power systems applications.
Bio: Alyssa Kody is a Ph.D. candidate in the Department of Electrical Engineering and Computer Science at the University of Michigan. Her research interests are at the intersection of control, optimization, and energy systems. Ms. Kody earned her M.S. in electrical engineering from the University of Michigan and a B.S. in civil engineering from Tufts University.