System Identification and Control Using Lyapunov-Based Deep Neural Networks without Persistent Excitation: A Concurrent Learning Approach

TL;DR

This paper introduces a novel Lyapunov-based deep neural network control method that simultaneously achieves system identification and trajectory tracking without persistent excitation, ensuring convergence and improving approximation accuracy.

Contribution

It presents the first concurrent learning approach for DNN-based control that guarantees stability and convergence without persistent excitation, using new adaptation laws and Lyapunov analysis.

Findings

Achieved 40.5% to 73.6% improvement in function approximation over baseline.

Maintained similar tracking error and control effort while improving approximation.

Demonstrated robustness on various systems and trajectories.

Abstract

Deep Neural Networks (DNNs) are increasingly used in control applications due to their powerful function approximation capabilities. However, many existing formulations focus primarily on tracking error convergence, often neglecting the challenge of identifying the system dynamics using the DNN. This paper presents the first result on simultaneous trajectory tracking and online system identification using a DNN-based controller, without requiring persistent excitation. Two new concurrent learning adaptation laws are constructed for the weights of all the layers of the DNN, achieving convergence of the DNN's parameter estimates to a neighborhood of their ideal values, provided the DNN's Jacobian satisfies a finite-time 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 performed on a range of systems and trajectories, with the same initial and operating conditions, demonstrated 40.5% to 73.6% improvement in function approximation performance compared to the baseline, while maintaining a similar tracking error and control effort. Simulations evaluating function approximation capabilities on data points outside of the trajectory resulted in 58.88% and 74.75% improvement in function approximation compared to the baseline.