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

Chunbin Qin1, Xiaopeng Qiao1, Jinguang Wang1

  • 1School of Artificial Intelligence, Henan University, Zhengzhou 450000, China.

Entropy (Basel, Switzerland)
|June 24, 2022
PubMed
Summary
This summary is machine-generated.

This study presents a robust trajectory tracking control method for nonlinear systems using adaptive dynamic programming (ADP). The approach ensures system stability and state constraints even with uncertain disturbances.

Keywords:
adaptive dynamic programmingcontrol barrier functionrobust tracking controlstate constraints

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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.