Asymptotic tracking control for time-delay nonlinear systems with parametric uncertainties and full state constraints

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Robotics and Automation

Background:

• Time-delay systems present significant control challenges due to inherent system uncertainties and state constraints.
• Ensuring full state satisfaction and managing delayed states are critical for system stability and performance.
• Adaptive control strategies are essential for handling uncertainties in complex dynamic systems.

Purpose of the Study:

• To design an adaptive backstepping control for uncertain nonlinear systems with time delays and full state constraints.
• To develop a control scheme that guarantees asymptotic tracking performance and maintains all states within desired regions.
• To ensure the boundedness of all signals within the closed-loop system.

Main Methods:

• Utilizing tan-type barrier Lyapunov functions (tBLFs) to enforce full state constraints.
• Employing a Lyapunov-Krasovskii function to address the impact of time delays.
• Implementing a novel adaptive backstepping control scheme for system stabilization.

Main Results:

• The proposed control scheme successfully ensures full state constraints satisfaction.
• Asymptotic tracking performance is achieved for the time-delay uncertain nonlinear systems.
• The boundedness of all closed-loop system signals is rigorously guaranteed.
• The effectiveness is demonstrated on single degree of freedom (1-DOF) time-delay electrostatic microactuator systems.

Conclusions:

• The developed adaptive backstepping control effectively handles time delays and full state constraints in uncertain nonlinear systems.
• The integration of tBLFs and Lyapunov-Krasovskii functions provides a robust solution for complex control problems.
• The control strategy ensures reliable performance and stability, validated by microactuator system simulations.