Model free or data-driven control methods are suitable for real-time applications that involve nonlinear systems with uncertainties. Human-machine interaction problems include parametric and non-parametric uncertainties that are hard to model. An alternative to develop complex models to account for these uncertainties is to exploit input-output data recorded from the human and machine to improve the performance of the combined system. In this paper, a motorized functional electrical stimulation (FES) cycling system is used to illustrate a data-driven approach that leverages past input-output data to generate an estimate of the system's non-linearly parameterizable and uncertain dynamics. This estimate is computed using an estimation law motivated by a design tool from finite-time stability and used as an input into a feedback controller. The nonlinear controller that switches across the lower-limb muscle groups and an electric motor is designed to achieve a desired speed tracking objective. A Lyapunov-based stability analysis is used to prove an asymptotic result of the tracking and estimation errors.