An upper motor neuron lesion (UMNL) can be caused by various neurological disorders or trauma and leads to disabilities. Neuromuscular electrical stimulation (NMES) is a technique that is widely used for rehabilitation and restoration of motor function for people suffering from UMNL. Typically, stability analysis for closed-loop NMES ignores the modulated implementation of NMES. However, electrical stimulation must be applied to muscle as a modulated series of pulses. In this paper, a muscle activation model with an amplitude modulated control input is developed to capture the discontinuous nature of muscle activation, and an identification-based closed-loop NMES controller is designed and analyzed for the uncertain amplitude modulated muscle activation model. Semi-global uniformly ultimately bounded tracking is guaranteed. The stability of the closed-loop system is analyzed with Lyapunov-based methods, and a pulse frequency related gain condition is obtained. Experiments are performed with five able-bodied subjects to demonstrate the interplay between the control gains and the pulse frequency, and results are provided which indicate that control gains should be increased to maintain stability if the stimulation pulse frequency is decreased to mitigate muscle fatigue. For the first time, this paper brings together an analysis of the controller and modulation scheme.
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