Switching Function Analysis of DC-DC Converters under Pontryagin's Maximum Principle

This work derives the closed-form solution of the switching function for a DC-DC buck converter under Pon-tryagin's maximum principle to gain insights into the circuit parameters impact on the converters' dynamic performance. We also analyzed the boost converter switching function under the same principle. Using MatLab/Simulink to simulate typical converters, the results matched our analysis while suggesting that boost converters could achieve time-optimal states transition within a single switching similar to the case of buck converters.