LYAPUNOV FUNCTION GENERATION USING MACHINE LEARNING ON UNDERACTUATED NONÂ LINEARÂ SYSTEM

• Main Author: Haiyunnisa, Triya
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/85225
• Institution: Institut Teknologi Bandung

Underactuated systems, characterized by having fewer control inputs than degrees of freedom, pose significant challenges in control design. Lyapunov functions have been a cornerstone in the stability analysis of nonlinear systems. Traditional approaches rely on analytical methods to construct Lyapunov functions. This often involves guessing a suitable function and proving that it decreases along system trajectories. In this research, represent the Lyapunov function using a neural network. This method allows to capture the intricate dependencies between state variables and the Lyapunov function value, providing a more flexible and adaptable representation compared to traditional analytical forms. The neural network parameters are optimized iteratively using Random Forest and Gradient Boosting algorithms. By minimizing the Lyapunov risk, the optimization process ensures the Lyapunov function satisfies the stability conditions over a larger region of the state space, thus enlarging the Region of Attraction (RoA) and enhancing the stability and robustness of underactuated systems. The comparison between the optimized and given Lyapunov functions reveals the significant advantages of using a more complex, machine learning-based approach to stability analysis. While the given function derived using a Voting Regressor, offers simplicity and efficiency, it falls short in capturing the full complexity of the system dynamics. The optimized Lyapunov functions, with their detailed and non- linear surfaces, provide a far better understanding of stability, identifying larger regions of attraction and offering a more robust and comprehensive stability analysis. This study demonstrates the value of machine learning techniques in enhancing the precision and effectiveness of Lyapunov functions for underactuated systems.