A frequency domain method for optimal periodic control

We consider the problem of optimal periodic input design for Single Input Single Output (SISO) systems with possibly nonquadratic and nonconvex performance objectives. Such problems arise naturally in energy efficiency and energy conversion applications. We develop a frequency domain method that is particularly suited for distributed systems, in that the underlying transfer functions are not required to be rational. In particular, the computational complexity of the method depends on the order of the polynomial (nonquadratic) nonlinearities in the performance objective as well as the number of required harmonics, but is independent of the underlying system dimension. Our method utilizes recently developed Polynomial Homotopy Continuation (PHC) algorithms for efficient solution of the harmonic balance multinomial equations representing first order optimality conditions.