Neural networks-based adaptive control for nonlinear time-varying delays systems with unknown control direction

Area of Science:

• Control Theory
• Nonlinear Systems
• Artificial Intelligence

Background:

• Nonlinear systems with time-varying delays present significant control challenges.
• Unknown control direction and unmeasurable states complicate controller design.
• Existing methods often require restrictive assumptions like the Lipschitz condition.

Purpose of the Study:

• To develop a novel adaptive control strategy for nonlinear systems with time-varying delays and unknown control direction.
• To design a neural network-based state observer for accurate state estimation.
• To ensure system stability and minimize tracking errors.

Main Methods:

• An adaptive neural memoryless observer is designed, independent of time-delay knowledge.
• A Lyapunov-Krasovskii functional and backstepping method are employed for controller construction.
• A Nussbaum function is utilized to address unknown control direction.

Main Results:

• The proposed controller guarantees semi-global uniform ultimate boundedness of all signals.
• Tracking errors converge to a small neighborhood of zero.
• The approach relaxes the Lipschitz condition for nonlinear functions.

Conclusions:

• The developed neural network-based adaptive control is effective for nonlinear systems with time-varying delays and unknown control direction.
• The method accommodates systems with mismatching conditions and unmeasurable states.
• Simulation examples validate the approach's effectiveness and applicability.