Abstract for "An optimal control application in power electronics using numerical algebraic geometry" by D.J. Bates, A.G. Beccuti, I.A. Fotiou, and M. Morari

We present an application in power electronics using an approach from numerical algebraic geometry, namely the homotopy continuation method for solving systems of polynomial equations. The proposed algorithm breaks the computations associated with the optimal control problem into two parts. An off-line part, where certain structural information of the control problem is precomputed, and an on-line part, where numerical algebraic geometry is used to retrieve the optimal control input to the system in real time. The approach is fast, reliable, and has a probability one guarantee of finding the global optimal solution to the problem at hand.