Structured Deep Neural Network-Based Backstepping Trajectory Tracking Control for Lagrangian Systems
This work addresses stability issues in neural network controllers for robotics and mechanical systems, offering a method to ensure performance with theoretical guarantees, though it appears incremental in combining existing techniques.
The paper tackles the challenge of ensuring closed-loop stability in deep neural network-based controllers for Lagrangian systems by introducing a structured DNN controller that guarantees stability for any compatible parameters and provides explicit tracking error bounds, with simulations demonstrating effectiveness.
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.