TY - JOUR
T1 - Lyapunov-Based Real-Time and Iterative Adjustment of Deep Neural Networks
AU - Sun, Runhan
AU - Greene, Max L.
AU - Le, Duc M.
AU - Bell, Zachary I.
AU - Chowdhary, Girish
AU - Dixon, Warren E.
N1 - Funding Information:
Manuscript received October 23, 2020; revised January 6, 2021; accepted January 21, 2021. Date of publication January 28, 2021; date of current version June 24, 2021. This work was supported in part by NSF under Award 1509516; in part by the Office of Naval Research under Grant N00014-13-1-0151; and in part by Air Force Office of Scientific Research under Award FA9550-19-1-0169. Recommended by Senior Editor C. Seatzu. (Corresponding author: Runhan Sun.) Runhan Sun, Max L. Greene, Duc M. Le, and Warren E. Dixon are with the Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611 USA (e-mail: [email protected]; [email protected]; [email protected]; [email protected]).
Publisher Copyright:
© 2017 IEEE.
PY - 2022
Y1 - 2022
N2 - A real-time Deep Neural Network (DNN) adaptive control architecture is developed for general uncertain nonlinear dynamical systems to track a desired time-varying trajectory. A Lyapunov-based method is leveraged to develop adaptation laws for the output-layer weights of a DNN model in real-time while a data-driven supervised learning algorithm is used to update the inner-layer weights of the DNN. Specifically, the output-layer weights of the DNN are estimated using an unsupervised learning algorithm to provide responsiveness and guaranteed tracking performance with real-time feedback. The inner-layer weights of the DNN are trained with collected data sets to increase performance, and the adaptation laws are updated once a sufficient amount of data is collected. Building on the results in (Joshi and Chowdhary, 2019) and (Joshi et al., 2020), which focus on deep model reference adaptive control for linear systems with known drift dynamics and control effectiveness matrices, this letter considers general control-affine uncertain nonlinear systems. The real-time controller and adaptation laws enable the system to track a desired time-varying trajectory while compensating for the unknown drift dynamics and parameter uncertainties in the control effectiveness. A nonsmooth Lyapunov-based analysis is used to prove semi-global asymptotic tracking of the desired trajectory. Numerical simulation examples are included to validate the results, and the Levenberg-Marquardt algorithm is used to train the weights of the DNN.
AB - A real-time Deep Neural Network (DNN) adaptive control architecture is developed for general uncertain nonlinear dynamical systems to track a desired time-varying trajectory. A Lyapunov-based method is leveraged to develop adaptation laws for the output-layer weights of a DNN model in real-time while a data-driven supervised learning algorithm is used to update the inner-layer weights of the DNN. Specifically, the output-layer weights of the DNN are estimated using an unsupervised learning algorithm to provide responsiveness and guaranteed tracking performance with real-time feedback. The inner-layer weights of the DNN are trained with collected data sets to increase performance, and the adaptation laws are updated once a sufficient amount of data is collected. Building on the results in (Joshi and Chowdhary, 2019) and (Joshi et al., 2020), which focus on deep model reference adaptive control for linear systems with known drift dynamics and control effectiveness matrices, this letter considers general control-affine uncertain nonlinear systems. The real-time controller and adaptation laws enable the system to track a desired time-varying trajectory while compensating for the unknown drift dynamics and parameter uncertainties in the control effectiveness. A nonsmooth Lyapunov-based analysis is used to prove semi-global asymptotic tracking of the desired trajectory. Numerical simulation examples are included to validate the results, and the Levenberg-Marquardt algorithm is used to train the weights of the DNN.
KW - Adaptive control
KW - Lyapunov-based analysis
KW - deep neural networks
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U2 - 10.1109/LCSYS.2021.3055454
DO - 10.1109/LCSYS.2021.3055454
M3 - Article
AN - SCOPUS:85100474407
SN - 2475-1456
VL - 6
SP - 193
EP - 198
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
M1 - 9337905
ER -