An optimal control application in power electronics using numerical algebraic geometry

We present an optimal control application in power electronics using the homotopy continuation method for solving systems of polynomial equations. The proposed approach breaks the computations associated with the optimal control problem into two parts, an off-line and an on-line. In the off-line part, the approach solves a generic polynomial system by means of a linear homotopy and stores its solution. Then, the on-line part uses this solution and, given the initial state value, it calculates by means of a coefficient parameter homotopy the optimal control input of the problem. The approach exhibits a probability-one guarantee of finding the global optimal solution to the problem at hand.