Multilevel Selective Harmonic Modulation via Optimal Control

We consider the Selective Harmonic Modulation (SHM) problem, consisting in design of a staircase control signal with some prescribed frequency components. In this work, we propose novel methodology to address SHM as an optimal problem which admissible controls are piecewise constant functions, taking values only given finite set. order fulfill constraint, introduce cost functional affine penalization for control, which, by means Pontryagin’s maximum principle, makes have desired form. Moreover, addition term provides uniqueness and continuity solution respect target frequencies. Another advantage our approach is that number switching angles waveform need not be determined priori. Indeed, entire signal, therefore, it determines location switches. also provide numerical examples solved approach.