Nonlinear dynamics and uncertainty-aware control of prosthetic systems using Bayesian Neural Networks and finite-time disturbance compensation

This paper presents an uncertainty-aware control architecture for nonlinear dynamical systems, with a focus on lower-limb prosthetics. The framework integrates Bayesian Neural Networks (BNNs), Nonlinear Model Predictive Control (NMPC), and a finite-time disturbance observer to enhance robustness, quantify uncertainty, and improve computational efficiency. The BNN, trained on NMPC-generated trajectories, serves as both a surrogate controller and an uncertainty estimator by incorporating predictive variance into the control law. This adaptation lets the system adjust control efforts in response to unmodeled dynamics and external disturbances. The finite-time corrective channel further stabilizes the system by compensating for actuator faults and unknown perturbations in real time. Lyapunov-based analysis provides theoretical guarantees, ensuring asymptotic stability in the presence of bounded disturbances. Simulations on a prosthetic leg model demonstrate accurate stabilization, reliable trajectory tracking with out-of-distribution inputs, and enhanced disturbance rejection compared to conventional NMPC. Additional comparative studies and a sensitivity analysis of key hyperparameters, including BNN prior variance and observer gains, confirm the robustness, generality, and reproducibility of the framework. By blending nonlinear control, data-driven learning, and stability analysis, this work shows an interdisciplinary approach to adaptive and resilient control in complex systems, directly relevant to rehabilitation robotics and uncertain nonlinear environments.