Optimal control of switched systems: The case of a step-down DC-DC converter

In this paper we extend the development of these algorithms to include switching costs and state-variable constraints, and we apply them to voltage regulation in a stepdown DC-DC voltage converter. The circuit, shown in Figure 1, is controlled by the switch so as to regulate the capacitor voltage to a given reference value, vc,ref. Two problems are being considered: the first is cast in the framework of Pulse Width Modulation (PWM) with a given (constant) switching frequency, where we compute optimal duty ratios, and the second concerns the computation of an optimal switching schedule without assuming a constant switching frequency.