Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems.

Area of Science:

• Control Theory
• Nonlinear Systems
• Adaptive Control

Background:

• High-order nonlinear systems with strict-feedback form present significant control challenges.
• Unknown uncertainties in these systems necessitate robust adaptive control strategies.
• Fixed-time control offers faster convergence than traditional finite-time methods.

Purpose of the Study:

• To develop an adaptive fixed-time control scheme for high-order nonlinear systems.
• To address unknown uncertainties within the strict-feedback structure.
• To ensure finite-time stability with convergence time independent of initial states.

Main Methods:

• Design of a backstepping controller incorporating adaptive laws.
• Utilization of Lyapunov functions for stability analysis.
• Application of the fixed-time Lyapunov stability criterion.

Main Results:

• The proposed adaptive control scheme guarantees finite-time stability for the error system.
• Convergence time is demonstrated to be independent of the system's initial conditions.
• Simulation results validate the effectiveness of the developed control strategy.

Conclusions:

• The adaptive fixed-time control is effective for high-order nonlinear systems.
• The controller achieves finite-time convergence irrespective of initial states.
• This approach offers a robust solution for systems with unknown uncertainties.