Real-Time Modular Deep Neural Network-Based Adaptive Control of Nonlinear Systems

A real-time deep neural network (DNN) adaptive control architecture is developed for uncertain control-affine nonlinear systems to track a time-varying desired trajectory. A Lyapunov-based analysis is used to develop adaptation laws for the output-layer weights and develop constraints for inner-layer weight adaptation laws. Unlike existing works in neural network and DNN-based control, the developed method establishes a framework to simultaneously update the weights of multiple layers for a DNN of arbitrary depth in real-time. The real-time controller and weight update laws enable the system to track a time-varying trajectory while compensating for unknown drift dynamics and parametric DNN uncertainties. A nonsmooth Lyapunov-based analysis is used to guarantee semi-global asymptotic tracking. Comparative numerical simulation results are included to demonstrate the efficacy of the developed method.