Structured Deep Neural Network-Based Backstepping Trajectory Tracking Control for Lagrangian Systems

TL;DR

This paper presents a structured deep neural network controller for Lagrangian systems that guarantees stability and improves tracking performance, even with model uncertainties and disturbances, validated through simulations.

Contribution

It introduces a structured DNN controller ensuring stability for Lagrangian systems and provides explicit error bounds, advancing neural network control design.

Findings

Guarantees closed-loop stability for neural network controllers.

Provides explicit bounds on tracking errors.

Demonstrates effectiveness through simulations.

Abstract

Deep neural networks (DNN) are increasingly being used to learn controllers due to their excellent approximation capabilities. However, their black-box nature poses significant challenges to closed-loop stability guarantees and performance analysis. In this paper, we introduce a structured DNN-based controller for the trajectory tracking control of Lagrangian systems using backing techniques. By properly designing neural network structures, the proposed controller can ensure closed-loop stability for any compatible neural network parameters. In addition, improved control performance can be achieved by further optimizing neural network parameters. Besides, we provide explicit upper bounds on tracking errors in terms of controller parameters, which allows us to achieve the desired tracking performance by properly selecting the controller parameters. Furthermore, when system models are unknown, we propose an improved Lagrangian neural network (LNN) structure to learn the system dynamics and design the controller. We show that in the presence of model approximation errors and external disturbances, the closed-loop stability and tracking control performance can still be guaranteed. The effectiveness of the proposed approach is demonstrated through simulations.