Numerical Solution of Differential Algebraic and Integral Algebraic Equations for a DC-DC Boost Converter by the Least-Squares Method
In this study, starting from the integral differential model of a DC-DC boost converter with a PI controller, we construct two mathematical representations of the problem. First, the original system is transformed into a nonlinear differentialalgebraic equation (DAE) in order to clarify the role of the algebraic constraint in the control model of the DC-DC boost converter. Next, based on linearization around an operating point, an integral-algebraic equation (IAE) is established to describe the small-signal problem. For both representations, the least squares method (LSM) is proposed as a unified tool for constructing approximate solutions. The results show that, for the nonlinear DAE form of the DC-DC boost converter with PI controller, the LSM provides highly accurate approximations when compared with the reference solution obtained by the Runge-Kutta method of orders 4 and 5 (RK45). For the IAE model of the smallsignal problem, this study demonstrates that integral-algebraic equations arise naturally in power electronics, thus broadening the range of applications for this type of equation. In addition, we present the formulation and analysis of the LSM for the IAE form of the problem under consideration. The obtained results suggest a promising research direction for power electronics models with differential-algebraic and integral-algebraic structures, emphasizing the advantages of a global optimization-based approach in handling problems whose solutions may be influenced by singular points or special operating regimes. © 2026 IEEE.
Библиографическая ссылка
Vo, Van Truong, Chistyakova, Elena, Chistyakov, Victor, Dreglea, Aliona, Сидоров Д.Н., Wang, Liguo Numerical Solution of Differential Algebraic and Integral Algebraic Equations for a DC-DC Boost Converter by the Least-Squares Method // International Conference on Electrical, Computer, and Energy Technologies, ICECET 2026. DOI: 10.1109/ICECET65726.2026.11632766
