Adaptive prescribed-time tracking control with guaranteed performance for uncertain nonlinear systems with arbitrary...

Area of Science:

• Control Theory
• Nonlinear Systems
• Adaptive Control

Background:

• Existing adaptive control methods often require specific initial conditions or are limited to stabilization.
• Handling arbitrary initial errors without compromising performance is a significant challenge in nonlinear control.

Purpose of the Study:

• To develop a unified control framework for adaptive prescribed-time tracking control of uncertain strict-feedback nonlinear systems.
• To address arbitrary initial errors while guaranteeing performance and achieving exact prescribed-time convergence.
• To ensure guaranteed transient performance alongside prescribed-time convergence.

Main Methods:

• A novel generalized tanh-based error transformation technique to decouple performance from initial errors.
• An enhanced adaptive backstepping framework incorporating fractional-order terms.
• Rigorous theoretical analysis to demonstrate uniform ultimate boundedness of closed-loop signals.

Main Results:

• Arbitrary initial errors are confined within asymmetric prescribed performance bounds.
• Tracking error enters the prescribed performance region before a user-specified time and converges to zero at a prescribed settling time.
• Guaranteed transient performance and prescribed-time convergence are achieved under system uncertainties.

Conclusions:

• The proposed control framework effectively handles uncertain nonlinear systems with arbitrary initial conditions.
• The method ensures exact prescribed-time convergence and guaranteed transient performance.
• Simulation results validate the effectiveness of the adaptive prescribed-time tracking control strategy.