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Recent studies suggest that deep neural networks (DNNs) have the potential to outperform neural networks (NNs) in approximating complex dynamics, which may enhance the tracking performance of a control system. However, unlike NN-based nonlinear control systems, designing update policies for the inner-layer weights of a DNN using Lyapunov-based stability methods is problematic since the inner-layer weights are nested within activation functions. Traditional DNN training methods (e.g., gradient descent) may improve the approximation capability of a DNN and thus could enhance a DNN-based controller’s tracking performance; however, traditional DNN-based control approaches lack stability guarantees and may be ineffective in training the DNN without large data sets, which could hinder the tracking performance. In this work, a DNN-based control structure is developed for a hybrid exoskeleton, which combines a rehabilitative robot with functional electrical stimulation (FES). The proposed control system updates the DNN weights in real-time and a rigorous Lyapunov-based stability analysis is performed to ensure semi-global asymptotic trajectory tracking, even without the presence of a data set. Specifically, a Lyapunov-based update law is developed for the output-layer DNN weights and Lyapunov-based constraints are established for the adaptation laws of the inner-layer DNN weights. Additionally, the DNN-based FES controller was designed to be saturated to increase the comfort and safety of the participant. 

Functional electrical stimulation (FES) is widely used for rehabilitating individuals with total or partial limb paralysis, but challenges like muscle fatigue and discomfort limit its effectiveness. Hybrid exoskeletons combine the rehabilitative benefits of exoskeletons and FES, while mitigating the drawbacks of each. However, despite hybrid exoskeletons being highly effective in rehabilitation, the dynamics associated with these systems are complex. Deep neural networks (DNNs) can approximate these complex hybrid exoskeleton dynamics; however, they traditionally lack stability guarantees and robustness, hindering their application in real-world systems. Moreover, traditional training methods (e.g., gradient descent) require an extensive dataset and offline training, further hindering a DNNs practical use. Therefore, this paper presents an innovative Lyapunov-based adaptation law, with a gradient descent-like structure, that is designed to update all layer weights of a DNN in real-time for a DNN-based hybrid exoskeleton control framework. To promote user comfort and safety, a saturation limit was implemented on the DNN-based FES controller and the excess control effort was redirected to the exoskeleton. A Lyapunov-based stability analysis was performed on the DNN-based hybrid exoskeleton control system to prove global asymptotic trajectory tracking. A numerical simulation of the designed controller was performed to validate the results. 

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. 

People suffering from neurological conditions (NCs) can benefit from motorized functional electrical stimulation (FES)-based rehabilitation equipment, called hybrid exoskeletons. These hybrid exoskeletons incorporate muscle-motor interaction that requires both the control of human muscles (i.e., FES) and robot motors to obtain a desirable performance. Two types of controllers (deep neural networks (DNN)-based and Admittance-based) were developed in this paper for a hybrid exoskeleton to control both human muscles and the exoskeleton’s motors. The uncertain dynamics of the hybrid exoskeleton are approximated by DNN to enable efficient FES control. The approximated DNN weights and biases were implemented in a control law where they were updated in multiple timescales. Specifically, the inner-layer DNN weights were updated iteratively offline while the outer-layer weights were updated online in real-time. The update law for the output-layer DNN weights was augmented with a concurrent learning (CL) inspired term to improve the learning performance of the DNN and, consequently, the overall system performance. The admittance-based motor controller uses torque feedback and desired torque contribution from the participant to modify the motor’s desired trajectory without forcing the participant to follow along predetermined trajectories and to promote the overall safety of the system. A Lyapunov-based stability analysis was completed for both control systems to ensure overall system performance. 

Essential tremor (ET) is the most prevalent type of movement disorder responsible for inducing tremor in an individual’s limbs. Various scales, such as the Fahn-Tolosa-Marin (FTM) tremor rating scale and The Essential Tremor Rating Assessment Scale (TETRAS), have been developed and used by physicians to classify the severity of ET. While the FTM scale is highly utilized in ET severity diagnosis, it relies on subjective assessments of the tremor. TETRAS, on the other hand, provides a more quantitative analysis of ET severity by ranking the severity of the tremor based on tremor magnitude. However, TETRAS requires a trained professional (such as a neurologist) to be present, and even in such cases, physicians use TETRAS as a metric baseline to visually approximate the severity of the tremor. In this pilot study, a deep neural network (DNN)-based scale is developed to accurately classify ET severity without the presence of trained experts. To validate the developed DNN-based ET classification scale, a preliminary experiment is performed on a single healthy participant during a leg extension exercise. Tremor was artificially induced at the knee using a motorized lower-limb exoskeleton. To enable near real-time ET classification and to enable rapid DNN response, the DNN assessed the severity of ET every 0.5 seconds; utilizing the previous 0.5 seconds of knee-angle data for DNN training and ET severity classification. The results of the preliminary experiment showed that the DNN achieved a training accuracy of 94.80% and a validation accuracy of 95.18%. Additionally, the DNN achieved a training accuracy of 93.63% and a validation accuracy of 94.05% using computer generated knee-angle measurements.