Unknown time-varying input delay compensation for neuromuscular electrical stimulation

In the present work, a control method is developed to yield lower limb tracking with neuromuscular electrical stimulation (NMES), despite an unknown time-varying input delay intrinsic to NMES, uncertain nonlinear dynamics, and additive bounded disturbances. A novel filtered tracking error signal is designed to obtain a delay-free control expression in the closed-loop error system. Furthermore, the filtered tracking error signal removes the requirement of exact knowledge of the input delay in the control design. The control development is based on an approach that uses Lyapunov-Krasovskii functionals in a Lyapunov-based stability analysis to prove ultimately bounded tracking error signals. Experimental results are provided to demonstrate the performance of the developed controller.