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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.
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This content will become publicly available on October 1, 2026
L-GraD: Lyapunov-Based Gradient of a Deep Neural Network-Based Upper-Extremity Exoskeleton Controller
Robotic exoskeletons provide a promising approach into improving traditional stroke rehabilitation with unique interactions and sensing modalities. In this article, we explore the use of deep neural networks (DNNs) as function estimators for any unmodeled dynamics especially in highly nonlinear system. Using the Lyapunov stability theory, the Lyapunov-based gradient descent (L-GraD) controller was designed to feed a desired reference trajectory into an impedance-controlled system. Adjusting DNN weights in real-time improves the tracking performance, and with the highly transparent and compliant exoskeleton, has potential for successful clinical implementation. Monte Carlo simulation results show that real-time DNNs for nonlinear dynamics improve the control performance and reduce the mean squared error during disturbance episodes. Results indicate a DNN with three hidden layers and 15 neurons each will provide the best results while maintaining lightweight architecture. Experimental results validate this L-GraD controller with improved performance over traditional control methods.
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- Award ID(s):
- 2230971
- PAR ID:
- 10651809
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- ASME Letters in Dynamic Systems and Control
- Volume:
- 5
- Issue:
- 4
- ISSN:
- 2689-6117
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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