Concurrent Learning for System Identification and Control Using Lyapunov-Based Deep Neural Networks

This paper presents the first result that enables the use of a concurrent learning (CL) adaptation law for the weights of all the layers of the DNN-based controller applied to a class of second-order control-affine systems. The developed CL-based adaptation achieves convergence of the DNN’s parameter estimates to a neighborhood of their ideal values, provided the DNN’s Jacobian satisfies a finite excitation condition. A Lyapunov-based stability analysis is conducted to ensure convergence of the tracking error, weight estimation errors, and observer errors to a neighborhood of the origin. Simulations demonstrated approximately 40% improvement in function approximation performance and over 65% improvement on off-trajectory evaluations compared to a baseline without CL.