An exact and approximate schur complement method for time-harmonic optimal control problems

Abstract

Time-harmonic control problems, constrained by a linear differential equation, can be solved efficiently by utilizing a Fourier time series expansion in the angular frequency variable. Then the optimal solution consists of a series of complex variable space discretization equations, which are uncoupled with respect to the different frequencies. Hence, it suffices to consider a single equation with the angular frequency as a parameter. We consider here methods to solve the so-arising linear system of equations and describe, analyze and test the performance of two novel approaches based on its exact and approximate Schur complement. The performance of the methods is tested and compared with another existing method.