Composite Adaptive Lyapunov-Based Deep Neural Network (Lb-DNN) Controller

TL;DR

This paper introduces a novel composite adaptive Lyapunov-based deep neural network controller that guarantees improved parameter estimation and stability, demonstrated through simulations showing significant performance enhancements.

Contribution

It presents the first composite adaptation method for Lyapunov-based DNN controllers, incorporating Jacobian and prediction error for better parameter convergence guarantees.

Findings

Guarantees on tracking, observer, and parameter errors are established.

Stronger performance when DNN Jacobian satisfies PE condition.

Simulation results show significant performance improvements.

Abstract

Recent advancements in adaptive control have equipped deep neural network (DNN)-based controllers with Lyapunov-based adaptation laws that work across a range of DNN architectures to uniquely enable online learning. However, the adaptation laws are based on tracking error, and offer convergence guarantees on only the tracking error without providing conclusions on the parameter estimation performance. Motivated to provide guarantees on the DNN parameter estimation performance, this paper provides the first result on composite adaptation for adaptive Lyapunov-based DNN controllers, which uses the Jacobian of the DNN and a prediction error of the dynamics that is computed using a novel method involving an observer of the dynamics. A Lyapunov-based stability analysis is performed which guarantees the tracking, observer, and parameter estimation errors are uniformly ultimately bounded (UUB), with stronger performance guarantees when the DNN's Jacobian satisfies the persistence of excitation (PE) condition. Comparative simulation results demonstrate a significant performance improvement with the developed composite adaptive Lb-DNN controller in comparison to the tracking error-based Lb-DNN.