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 [1] and [2], which focus on deep model reference adaptive control for linear systems with known drift dynamics and control effectiveness matrices, this paper 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.

Original languageEnglish (US)
JournalIEEE Control Systems Letters
StateAccepted/In press - 2021


  • Adaptive control
  • Adaptive control
  • Artificial neural networks
  • Lyapunov-based analysis.
  • Nonlinear dynamical systems
  • Real-time systems
  • Stability analysis
  • Training
  • Trajectory
  • deep neural networks

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization

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