Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain...

Area of Science:

• Control Systems Engineering
• Nonlinear System Dynamics
• Artificial Intelligence in Control

Background:

• Trajectory tracking is crucial for nonlinear systems but challenging due to state constraints and disturbances.
• Existing methods often struggle to guarantee safety and robustness simultaneously.

Purpose of the Study:

• To propose a robust trajectory tracking control method for nonlinear systems.
• To address state constraints and uncertain disturbances using adaptive dynamic programming.
• To ensure system safety and stability.

Main Methods:

• Formulated tracking control as a robust control adjustment problem for an augmented system.
• Transformed the guaranteed cost tracking control problem into an optimal control problem.
• Developed a novel safe Hamilton-Jacobi-Bellman (HJB) equation by integrating cost functions and control barrier functions (CBF).
• Employed a critic neural network (NN) to approximate the solution of the safe HJB equation.
• Utilized Lyapunov stability theory to guarantee uniform ultimate boundedness (UUB) of system states and NN parameters.

Main Results:

• The proposed method effectively handles state constraints and uncertain disturbances.
• The critic NN successfully approximates the solution to the safe HJB equation.
• Lyapunov stability theory confirms uniform ultimate boundedness (UUB) for system states and NN parameters.
• Simulation results validate the feasibility and performance of the proposed robust control strategy.

Conclusions:

• The developed adaptive dynamic programming (ADP) based robust control method ensures trajectory tracking for nonlinear systems under state constraints and disturbances.
• The integration of control barrier functions (CBF) into the HJB equation provides a mechanism for enforcing safety regulations.
• The method offers a promising approach for robust and safe control of complex nonlinear systems.