Cycling induced by functional electrical stimulation (FES) with motorized assistance is a rehabilitative approach for individuals with movement impairments. In this paper, an adaptive controller is designed for cadence tracking by switching across multiple muscle groups and an electric motor. The control design and analysis are based on a recently developed adaptive method called integral concurrent learning and an invariance-like tool to ensure stability of switched adaptive systems. A Lyapunov-based stability analysis for the overall switched rider-cycle system is segregated into two phases. During the first phase when sufficient learning has not been attained, which is quantified by a finite excitation condition, global asymptotic tracking and bounded parameter estimation are guaranteed. In the second phase, global exponential tracking and parameter convergence is ensured after the finite excitation condition is satisfied for all the subsystems within a finite time.