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1. Concurrent Learning and Lyapunov-Based Updates of Deep Neural Networks for Euler-Lagrange Dynamic Systems

   https://doi.org/10.23919/ACC60939.2024.10644154  

   Basyal, Sujata; Ting, Jonathan; Mishra, Kislaya; Allen, Brendon C (July 2024, IEEE)

   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. 

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2. Concurrent Learning Augmented DNN-Based and Admittance Control of a Hybrid Exoskeleton

   https://doi.org/10.1109/ICORR66766.2025.11063179  

   Basyal, Sujata; Mishra, Kislaya; Ting, Jonathan; Allen, Brendon (May 2025, IEEE)

   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. 

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3. Real-time Modular Adjustment of Inner-Layer Weights of a Deep Neural Network-based Saturated Lower Limb Hybrid Exoskeleton Controller

   https://doi.org/10.23919/ACC63710.2025.11107714  

   Ting, Jonathan; Mishra, Kislaya; Basyal, Sujata; Allen, Brendon C (July 2025, IEEE)

   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. 

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4. Deep Neural Network Based Saturated Adaptive Control of Muscles in a Lower-Limb Hybrid Exoskeleton

   https://doi.org/10.1115/IMECE2023-112415  

   Ting, Jonathan A; Basyal, Sujata; Allen, Brendon C (October 2023, American Society of Mechanical Engineers)

   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. 

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5. L-GraD: Lyapunov-based Gradient Descent of a DNN-based Hybrid Exoskeleton Controller

   https://doi.org/10.23919/ACC63710.2025.11107845  

   Ting, Jonathan; Basyal, Sujata; Mishra, Kislaya; Allen, Brendon C (July 2025, IEEE)

   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. 

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