Sampled-Data Observer Based Dynamic Surface Control of Delayed Neuromuscular Functional Electrical Stimulation

Functional electrical stimulation (FES) is a potential technique for reanimating paralyzed muscles post neurological injury/ disease. Several technical challenges including difficulty in measuring and compensating for delayed muscle activation levels inhibit its satisfactory control performance. In this paper, an ultrasound (US) imaging approach is proposed to measure delayed muscle activation levels under the implementation of FES. Due to low sampling rates of US imaging, a sampled data observer (SDO) is designed to estimate the muscle activation in a continuous manner. The SDO is combined with continuous-time dynamic surface control (DSC) approach that compensates for the electromechanical delay (EMD) in the tibialis anterior (TA) activation dynamics. The stability analysis based on the Lyapunov-Krasovskii function proves that the SDObased DSC plus delay compensation (SDO-DSC-DC) approach achieves semi-global uniformly ultimately bounded (SGUUB) tracking performance. Simulation results on an ankle dorsiflexion neuromusculoskeletal system show the root mean square error (RMSE) of desired trajectory tracking is reduced by 19.77 % by using the proposed SDO-DSC-DC compared to the DSC-DC without the SDO. The findings provide potentials for rehabilitative devices, like powered exoskeleton and FES, to assist or enhance human limb movement based on the corresponding muscle activities in real-time.