Gradient Descent-Barzilai Borwein-Based Neural Network Tracking Control for Nonlinear Systems With Unknown Dynamics.

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Nonlinear Dynamics

Background:

• Nonlinear systems present significant challenges in control due to unknown drift and control input gain functions.
• Traditional control methods often require precise system models and extensive parameter tuning.
• Neural networks offer a powerful tool for approximating complex system dynamics and control laws.

Purpose of the Study:

• To propose a novel output tracking control strategy for nonlinear systems with unknown dynamics.
• To enhance controller design by directly approximating the controller using a neural network.
• To improve the efficiency and reduce the complexity of controller parameter tuning.

Main Methods:

• A combined gradient descent-Barzilai Borwein (GD-BB) algorithm and radial basis function neural network (RBFNN) were employed.
• Neural network parameters (weights, centers, widths) and learning rates were updated online using a GD-BB-based learning algorithm.
• The controller was directly approximated by the neural network, simplifying the design process.

Main Results:

• The proposed strategy successfully updated neural network parameters and learning rates online.
• The controller design process was simplified, significantly reducing the number of tunable parameters.
• Theoretical analysis confirmed the stability of the closed-loop system.
• Simulations on discrete-time and inverted pendulum systems validated the control strategy's effectiveness.

Conclusions:

• The combined GD-BB and RBFNN control strategy offers an effective approach for nonlinear systems with unknown dynamics.
• Online updating of NN parameters and learning rates simplifies controller design and enhances stability.
• The proposed method demonstrates practical applicability through successful simulations on benchmark systems.