Switched Adaptive Integral Concurrent Learning for Powered FES-Cycling

Jonathan Casas, Chen Hao Chang, Steven W. Brose, Victor H. Duenas

Research output: Contribution to journalArticlepeer-review


Functional electrical stimulation (FES) and motorized cycles have the potential to recover lost function and mobility in people with neurological disorders. However, the human-robot system is uncertain, nonlinear, and time-varying, posing technical challenges to customizing the interaction across participants. In this paper, a closed-loop switching adaptive controller is designed to achieve cadence tracking using a powered FES-cycling system. The adaptive design copes with the parametric uncertainty of the cycle-rider dynamics and the unknown switching muscle control effectiveness by computing estimates of the uncertain parameters. A saturated state-feedback controller activates the quadriceps muscle groups, whereas an integral concurrent learning technique activates the electrical motor and leverages input-output data to estimate the parametric uncertainty and achieve cadence tracking. A switching Lyapunov-based stability analysis is developed in two phases. The initial phase ensures bounded tracking and estimation when a learning condition has not been attained; in the second phase, global exponential tracking and estimation convergence is ensured, given an online-verified finite excitation condition is satisfied. The developed controller was tested during three FES-cycling trials with different cadence trajectories and learning conditions in eight able-bodied individuals and three participants with neurological conditions (NCs) during ten-minute and five-minute experiments, respectively. The system achieves an average RMS cadence tracking error of <inline-formula> <tex-math notation="LaTeX">$2.49\pm0.42$</tex-math> </inline-formula>, <inline-formula> <tex-math notation="LaTeX">$2.66\pm0.36$</tex-math> </inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$2.69\pm0.58$</tex-math> </inline-formula> revolutions per minute (RPM) with the able-bodied participants, while an average RMS cadence tracking error of <inline-formula> <tex-math notation="LaTeX">$3.15\pm0.97$</tex-math> </inline-formula>, <inline-formula> <tex-math notation="LaTeX">$2.60\pm0.17$</tex-math> </inline-formula>, <inline-formula> <tex-math notation="LaTeX">$3.47\pm1.43$</tex-math> </inline-formula> RPM for the participants with NCs in three cycling trials. <italic>Note to Practitioners</italic>&#x2014;FES-Cycling is a rehabilitation strategy recommended to recover muscle capacity and improve cardiovascular function in people with neurological disorders. Although significant progress has been made on the closed-loop control of FES-cycling systems, a critical need exists to develop adaptive strategies to comply with the nonlinear, time-varying muscle responses to FES, cope with the uncertain parameters of the cycle-rider system, and improve tracking performance. This paper develops a decoupled control design for muscles and motor. The FES controller is tuned using minimal parameters to yield bounded muscle responses with a tunable saturation limit. The electric motor control is designed using an adaptive-based method that estimates the uncertain parameters in the cycle-rider system and strategically exploits the muscle input to improve tracking performance. Results from cycling trials in able-bodied individuals and participants with neurological conditions demonstrate the feasibility of the adaptive control design to tracking different trajectories with the same set of control parameters across all participants despite the inherent variability in human subjects. The adaptive controller requires minimal tuning and copes with the rider&#x2019;s uncertainty while obtaining predictable, satisfactory performance, potentially paving the way for the widespread implementation of adaptive closed-loop controllers for FES-cycling systems at the clinic and community.

Original languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalIEEE Transactions on Automation Science and Engineering
StateAccepted/In press - 2023


  • Adaptive control
  • Adaptive control
  • assistive robotics
  • Kinematics
  • Muscles
  • Switches
  • switching systems
  • Torque
  • Trajectory
  • Uncertainty

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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