Extremum Seeking Control for Power Tracking via Functional Electrical Stimulation

Abstract

Abstract Motorized Functional Electrical Stimulation (FES)-cycling is a promising rehabilitative strategy for people possessing movement disorders as a result of neurological conditions. Cadence and torque (power) tracking objectives have been previously prescribed in FES-cycling to exploit the functional benefits of neuromuscular electric stimulation and produce intensive active therapy with motorized assistance. However, predetermined desired trajectories for either objective may yield sub-optimal training performance since the movement capacity of a person recovering from injury is unknown and time-varying. Hence, online adaptation is well-motivated to determine optimal cadence and torque trajectories. In this paper, an extremum seeking control (ESC) algorithm is implemented in real-time to compute the optimal cadence and torque trajectory (i.e., the peak torque demand) to maximize power output in an FES-cycling protocol. The uncertain, nonlinear FES-cycle system is an autonomous, state-dependent switched system to activate lower-limb muscles and an electric motor. Torque tracking is achieved by electrically stimulating the muscles via a learning controller and cadence tracking by engaging an electric motor. A passivity-based approach is utilized to analyze the stability of both tracking objectives.