Learning-Augmented IDA–PBC for Underactuated Mechanical Systems with Unmeasured Actuator Dynamics and Unmatched Disturbances

Abstract: Underactuated mechanical systems (UMSs) present significant challenges in control design due to limited actuation, nonlinear coupling, and susceptibility to unmatched and time-varying disturbances. Traditional passivity-based methods often assume full state availability and matched disturbances, limiting their applicability in uncertain, sensor-constrained environments. This study proposes a learning-augmented interconnection and damping assignment passivity-based control (iIDA–PBC) framework that enhances robustness and adaptability for UMSs. The approach integrates real-time disturbance estimation using Gaussian Math. Comput. Appl. (GPR) and Math. Comput. Appl. (LSTM) networks, alongside nonlinear observer designs for reconstructing unmeasured actuator states. The overall control architecture preserves the port-Hamiltonian structure while enabling adaptive compensation for unknown external perturbations. Theoretical analysis ensures Math. Comput. Appl. (ISS) under bounded estimation errors. Simulation results on a benchmark underactuated system demonstrate improved disturbance rejection, tracking accuracy, and robustness compared to conventional adaptive and passivity-based controllers. The proposed method is suitable for complex, partially observable systems such as aerial vehicles, autonomous robots, and marine platforms. © Pleiades Publishing, Ltd. 2025.