Deep Neural Network-Based Adaptive FES-Cycling Control: A Hybrid Systems Approach

Functional electrical stimulation (FES)-cycling is a rehabilitation method for restoration of motor function in individuals with neuromuscular disorders. FES-cycling control faces challenges due to the nonlinear behavior and unstructured uncertainty of the rider's muscle dynamics. Moreover, there exist regions in the crank cycle at which it is not kinematically efficient to stimulate certain muscles. To maximize torque output, the stimulation pattern is designed such that the FES control input switches between the different muscle groups. The resulting continuous-time and discrete-time characteristics motivate a hybrid systems approach. In this paper, a deep neural network (DNN)-based adaptive closed-loop hybrid control scheme is developed for the rider-cycle system. A hybrid system is formulated to model the hybrid behavior of both the FES-cycling system and adaptive DNN updates. Unknown dynamics of the system are approximated using a feedforward DNN estimate in the developed motor input controller, and a Lyapunov stability-derived weight adaptation law is developed for real-time estimation of the DNN outer-layer weights. Asymptotic convergence of the position and cadence tracking errors is guaranteed with a hybrid systems analysis using Lyapunov-based techniques.