Deep Neural Network-Based Approximate Optimal Tracking for Unknown Nonlinear Systems

The infinite horizon optimal tracking problem is solved for a deterministic, control-affine, unknown nonlinear dynamical system. A deep neural network (DNN) is updated in real time to approximate the unknown nonlinear system dynamics. The developed framework uses a multitimescale concurrent learning-based weight update policy, with which the output layer DNN weights are updated in real time, but the internal DNN features are updated discretely and at a slower timescale (i.e., with batch-like updates). The design of the output layer weight update policy is motivated by a Lyapunov-based analysis, and the inner features are updated according to existing DNN optimization algorithms. Simulation results demonstrate the efficacy of the developed technique and compare its performance to existing techniques.