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

Area of Science:

• Robotics and Control Systems
• Machine Learning Applications
• Nonlinear Control Theory

Background:

• Deep neural networks (DNNs) offer powerful function approximation for control but lack inherent stability guarantees due to their black-box nature.
• Ensuring closed-loop stability and performance analysis for DNN-based controllers in complex systems remains a significant challenge.

Purpose of the Study:

• To develop a structured deep neural network (DNN)-based controller for trajectory tracking in Lagrangian systems.
• To provide formal guarantees for closed-loop stability and performance analysis of the proposed DNN controller.
• To address scenarios with unknown system dynamics and external disturbances.

Main Methods:

• Utilized backing techniques to design a structured DNN controller for Lagrangian systems.
• Incorporated explicit upper bounds on tracking errors based on controller parameters.
• Proposed an improved Lagrangian neural network (LNN) structure for learning system dynamics when models are unknown.

Main Results:

• The structured DNN controller ensures closed-loop stability for any compatible neural network parameters.
• Improved control performance is achievable through neural network parameter optimization.
• Tracking errors can be bounded, allowing for desired performance by selecting appropriate controller parameters.
• Closed-loop stability and tracking performance are maintained despite model approximation errors and external disturbances.

Conclusions:

• The proposed structured DNN-based controller effectively addresses stability and performance limitations of traditional DNN controllers for Lagrangian systems.
• The approach offers a robust solution for trajectory tracking, even in the presence of model uncertainties and disturbances.
• Explicit error bounds and parameter selection provide practical guidelines for achieving desired control performance.