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A deep neural network (DNN)-based adaptive controller with a real-time and concurrent learning (CL)-based adaptive update law is developed for a class of uncertain, nonlinear dynamic systems. The DNN in the control law is used to approximate the uncertain nonlinear dynamic model. The inner-layer weights of the DNN are updated offline using data collected in real-time; whereas, the output-layer DNN weights are updated online (i.e., in real-time) using the Lyapunov- and CL-based adaptation law. Specifically, the inner-layer weights of the DNN are trained offline (concurrent to real-time execution) after a sufficient amount of data is collected in real-time to improve the performance of the system, and after training is completed the inner-layer DNN weights are updated in batch-updates. The key development in this work is that the output-layer DNN update law is augmented with CL-based terms to ensure that the output-layer DNN weight estimates converge to within a ball of their optimal values. A Lyapunov-based stability analysis is performed to ensure semi-global exponential convergence to an ultimate bound for the trajectory tracking errors and the output-layer DNN weight estimation errors. 

This paper presents a deep neural network (DNN)-and concurrent learning (CL)-based adaptive control architecture for an Euler-Lagrange dynamic system that guarantees system performance for the first time. The developed controller includes two DNNs with the same output-layer weights to ensure feasibility of the control system. In this work, a Lyapunov-and CL-based update law is developed to update the output-layer DNN weights in real-time; whereas, the inner-layer DNN weights are updated offline using data that is collected in real-time. A Lyapunov-like analysis is performed to prove that the proposed controller yields semi-global exponential convergence to an ultimate bound for the output-layer weight estimation errors and for the trajectory tracking errors. 

Hybrid exoskeletons are used to blend the rehabilitative efficacy and mitigate the shortcomings of functional electrical stimulation (FES) and exoskeleton-based rehabilitative solutions. This paper introduces a novel nonlinear controller that may potentially improve the rehabilitative efficiency of a lower limb hybrid exoskeleton by implementing four key features into the FES and exoskeleton controllers. First, the FES input to the user’s muscles is saturated based on user preference to ensure user comfort. Second, rather than discarding the excess control effort from the saturated FES input, it is redirected into the exoskeleton’s motor controller. Third, a safe deep neural network (DNN) is designed to estimate the unknown dynamics of the hybrid exoskeleton and the DNN is implemented in the FES controller to improve the control efficiency and tracking performance. Fourth, an adaptive update law is designed to estimate the unknown muscle control effectiveness to facilitate the implementation of the DNN. Lyapunov stability-based methods are used to generate real-time adaptive update laws that will train the adaptive estimate of the muscle effectiveness and the output layer weights of the DNN in real-time, ensure the effectiveness and safety of the controllers, and prove global asymptotic tracking of the desired trajectory. 

Introduction: Functional electrical stimulation (FES) induced cycling has been shown to be an effective rehabilitation for those with lower limb movement disorders. However, a consequence of FES is an electromechanical delay (EMD) existing between the stimulation input and the onset of muscle force. The objective of this study is to determine if the cycle crank angle has an effect on the EMD. Methods: Experiments were performed on 10 participants, five healthy and five with neurological conditions resulting in movement disorders. A motor fixed the crank arm of a FES-cycle in 10 degree increments and at each angle stimulation was applied in a random sequence to a combination of the quadriceps femoris and gluteal muscle groups. The EMD was examined by considering the contraction delay (CD) and the residual delay (RD), where the CD (RD) is the time latency between the start (end) of stimulation and the onset (cessation) of torque. Two different measurements were used to examine the CD and RD. Further, two multiple linear regressions were performed on each measurement, one for the left and one for the right muscle groups. Results: The crank angle was determined to be statistically relevant for both the CD and RD. Conclusions: Since the crank angle has a significant effect on both the CD and RD, the angle has a significant effect on the EMD. Therefore, future efforts should consider the importance of the crank angle when modelling or estimating the EMD to improve control designs and ultimately improve rehabilitative treatments. 

Functional electrical stimulation (FES) induced cycling is a common rehabilitative technique applied for those with a movement disorder. An FES cycle system is a nonlinear switched dynamic system that has a potentially destabilizing input delay between stimulation and the resulting muscle force. In this paper, a dual objective control system for a nonlinear, uncertain, switched FES cycle system with an unknown time-varying input delay is developed and a Lyapunov-like dwell-time analysis is performed to yield exponential power tracking to an ultimate bound and global exponential cadence tracking. Preliminary experimental results for a single healthy individual are provided and demonstrate average power and cadence tracking errors of -0.05 ± 0.80 W and -0.05 ± 1.20 RPM, respectively, for a target power of 10 W and a target cadence of 50 RPM. 

A common rehabilitative technique for those with neuro-muscular disorders is functional electrical stimulation (FES) induced exercise such as FES-induced biceps curls. FES has been shown to have numerous health benefits, such as increased muscle mass and retraining of the nervous system. Closed-loop control of a motorized FES system presents numerous challenges since the system has nonlinear and uncertain dynamics and switching is required between motor and FES control, which is further complicated by the muscle having an uncertain control effectiveness. An additional complication of FES systems is that high gain feedback from traditional robust controllers can be uncomfortable to the participant. In this paper, data-based, opportunistic learning is achieved by implementing an integral concurrent learning (ICL) controller during a motorized and FES-induced biceps curl exercise. The ICL controller uses adaptive feedforward terms to augment the FES controller to reduce the required control input. A Lyapunov-based analysis is performed to ensure exponential trajectory tracking and opportunistic, exponential learning of the uncertain human and machine parameters. In addition to improved tracking performance and robustness, the potential of learning the specific dynamics of a person during a rehabilitative exercise could be clinically significant. Preliminary simulation results are provided and demonstrate an average position error of 0.14 ± 1.17 deg and an average velocity error of 0.004 ± 1.18 deg/s.