Closed-Loop Neuromuscular Electrical Stimulation Method Provides Robustness to Unknown Time-Varying Input Delay in Muscle Dynamics

Neuromuscular electrical stimulation (NMES) is commonly used to rehabilitate people with motor impairment (e.g., following stroke or spinal cord injury). Closed-loop NMES holds the promise to facilitate coordinated limb motion, but technical challenges remain. In particular, there is a potentially destabilizing delay between the application of the electrical stimulation and the ensuing muscle contraction, which changes as muscle fatigues. In this brief, a closed-loop NMES method is developed to yield lower limb tracking, despite an unknown time-varying input delay, uncertain nonlinear limb dynamics, and additive bounded disturbances. A novel filtered error signal is designed using the past states in a finite integral over a constant estimated delay interval. The control development is based on an approach that uses Lyapunov–Krasovskii functionals in a Lyapunov-based stability analysis to prove ultimately bounded tracking. Experimental results in healthy individuals and participants with neurological conditions are provided to demonstrate the performance of the developed controller.