Lyapunov Function Generation Using Machine Learning for Underactuated System

Underactuated systems, characterized by fewer control inputs compared to their degrees of freedom, pose significant challenges in control design. Stabilization of underactuated nonlinear systems presents several challenges mainly due to their complex dynamic behavior and the presence of uncertainties. In this study, the representation of Lyapunov functions is done using artificial neural networks. The neural network parameters are optimized iteratively using random forest and gradient boosting algorithms. Based on the research results, the iteration process to obtain the Lyapunov function is also achieved quickly and the derivative of the Lyapunov function consistently decreases in all systems, becoming negative as the iteration progresses. In addition, several tests were carried out to assess the effectiveness of the method used to determine the Lyapunov function. From the analysis results, it was found that the area of the optimized Lyapunov function RoA expanded significantly more than 41.14% compared to previously estimated RoA area. The expansion of RoA through optimization indicates that the system is stronger and potentially more stable, assuming the Lyapunov condition applies in a wider area.