Contraction-based Controller for a MMC Based on Data-Driven Nonlinear Identification with Noisy Data

The widespread application of Modular Multilevel Converters (MMC) requires novel techniques and developments where the complexity and drawbacks about their control, modeling and analysis can be developed with recent directions. In this paper, we propose a novel approach in data-driven nonlinear identification techniques based on Koopman operator theory, Sparse regression, Regularization methods summarize by the so-called SINDy (Sparse Identification of Nonlinear Dynamics); according to this methodology, the initial stage of the method proposed, is to synthesize a suitable approximation of the MMC nonlinear dynamics based on data and Koopman theory, considering independent and identically distributed noise, once these dynamics are learnt, it follows with a nonlinear control design applying the contraction theory proving stability conditions of the closed-loop system dynamics. In this work, first, we establish some prior work and main contributions, then mathematical basis about nonlinear identification methods based on Koopman operator theory and Contraction theory for nonlinear systems are established. Then, we obtain the MMC dynamics for analysis and control and finally, we implement a numerical simulation validating the claims and advantages of the proposed study.