Robust tracking control of pulse-width modulated systems through multi-frequency averaging

The paper considers a class of pulse-width modulated systems with applications in switched mode power converters. An optimal control problem is posed where the objective is to minimize a cost integral defined on the continuous time output of the switched dynamical system. A dynamic Fourier series decomposition, where the Fourier coefficients are defined over a moving time window, is used to equivalently reformulate the hybrid control problem in the frequency domain. The frequency domain problem is truncated and linearized and thus reduces to a convex quadratic problem. The main advantage of the approach, compared to previous work on hybrid control of power converters, is that the frequency domain formulation can be made more robust to parameter uncertainty.