KAN-Hammerstein model and tube-based model predictive control for robust torque tracking with sEMG feedback in an FES-assisted rehabilitation system

Abstract

Functional electrical stimulation (FES) has shown promise in restoring motor functions for patients with spinal cord injury and stroke. However, its clinical application is limited by insufficient accuracy in modeling muscle dynamics and the lack of robust control strategies under complex disturbances. To address these challenges, this study proposes a closed-loop framework that integrates high-precision modeling with strong robustness. A Hammerstein model enhanced by Kolmogorov-Arnold Networks (KAN) is constructed, where the explicit mathematical representation of KAN significantly improves the nonlinear dynamic modeling of muscle behavior. Additionally, a forgetting factor recursive least squares (FFRLS) algorithm is employed for online identification of time-varying parameters, achieving improved performance over traditional approaches. Further, a sliding-mode tube model predictive control (SMC-Tube MPC) strategy driven by surface electromyography (sEMG) feedback is developed. By combining the disturbance rejection capability of sliding mode control with the state constraint handling features of Tube-MPC, the proposed controller enables stable torque tracking under complex perturbations. The framework is validated on an experimental platform integrating a dynamometer, sEMG acquisition device, and electrical stimulator. Experiments with healthy subjects demonstrate high accuracy and strong robustness of the proposed system.