Machine Learning-Assisted Synthesis of Self-Organizing SISO Control Systems with Guaranteed Lyapunov Stability

The proposed methodology combines analytical control laws with adaptive mechanisms and machine-learning-assisted modules based on regression trees, random forests, and extreme gradient boosting (XGBoost). Machine learning models are employed to approximate unknown nonlinear dynamics, compensate disturbances, and adjust controller parameters, while the overall control structure is constrained by Lyapunov stability conditions. This ensures that the inclusion of data-driven components does not violate the fundamental requirement of system stability. The effectiveness of the proposed approach is evaluated through simulation experiments across three operating modes with varying degrees of nonlinearity and dynamic complexity. The results show that hybrid models incorporating ensemble machine learning methods improved performance compared with the analytical and adaptive baselines examined. XGBoost-based control achieves the lowest error values and the highest level of Lyapunov stability compliance (up to 99.3%). The main contribution of this study lies in the development of a unified synthesis framework in which machine learning is not used as a standalone control strategy but as a machine-learning-assisted support mechanism integrated into a theoretically grounded control architecture. The proposed approach provides a balance between adaptability, accuracy, and rigorous stability guarantees, suggesting potential applicability to simulation-based and offline-assisted control design tasks, while real-time embedded implementation requires additional computational optimization and validation.