Asymptotic Tracking Control for Uncertain Nonlinear Strict-Feedback Systems With Unknown Time-Varying Delays

Area of Science:

• Control Theory
• Nonlinear Systems
• Adaptive Control

Background:

• Achieving asymptotic tracking control in uncertain nonlinear systems with unknown time-varying delays and unknown control direction is a significant challenge.
• Existing methods often struggle with singularity issues and computational complexity.

Purpose of the Study:

• To develop a robust and computationally efficient adaptive control scheme for uncertain nonlinear strict-feedback systems with unknown time-varying delays and unknown control direction.
• To ensure asymptotic convergence of the output tracking error and stability of the closed-loop system.

Main Methods:

• Utilizing a Lyapunov-Krasovskii functional (LKF) to effectively handle time delays.
• Employing neural networks (NN) to compensate for unknown terms arising from the LKF derivative.
• Constructing an NN-based adaptive control scheme using the backstepping technique.

Main Results:

• The proposed scheme achieves asymptotic tracking control for the addressed systems.
• The singularity issue commonly found in time-delay problems is resolved under milder conditions.
• All signals within the closed-loop system are proven to be semiglobally uniformly ultimately bounded.

Conclusions:

• The developed NN-based adaptive control scheme offers a simple structure and low computational cost.
• The method effectively handles unknown time-varying delays and unknown control direction in nonlinear systems.
• The approach provides improved transient performance and is validated through theoretical analysis and numerical simulations.