  Deep neural network (DNN)-based adaptive controllers can be used to
compensate for unstructured uncertainties in nonlinear dynamic systems.
However, DNNs are also very susceptible to overfitting and co-adaptation.
Dropout regularization is an approach where nodes are randomly dropped during
training to alleviate issues such as overfitting and co-adaptation. In this
paper, a dropout DNN-based adaptive controller is developed. The developed
dropout technique allows the deactivation of weights that are stochastically
selected for each individual layer within the DNN. Simultaneously, a
Lyapunov-based real-time weight adaptation law is introduced to update the
weights of all layers of the DNN for online unsupervised learning. A non-smooth
Lyapunov-based stability analysis is performed to ensure asymptotic convergence
of the tracking error. Simulation results of the developed dropout DNN-based
adaptive controller indicate a 38.32% improvement in the tracking error, a
53.67% improvement in the function approximation error, and 50.44% lower
control effort when compared to a baseline adaptive DNN-based controller
without dropout regularization.
