Fast funnel control based fixed-time consensus tracking for nonlinear multi-agent systems with unknown disturbances.

Area of Science:

• Control Systems Engineering
• Nonlinear Systems Theory
• Robotics and Automation

Background:

• Nonlinear multi-agent systems (NMASs) face challenges with unknown lumped disturbances.
• Achieving consensus tracking under uncertainty requires robust control strategies.
• Existing methods may suffer from singularity, slow convergence, or controller conservativeness.

Purpose of the Study:

• To develop a fixed-time consensus tracking control strategy for NMASs with unknown disturbances.
• To design a disturbance observer for accurate and rapid estimation of lumped uncertainties.
• To ensure fast convergence, bounded errors, and improved stability for the closed-loop system.

Main Methods:

• Design of a fixed-time sliding mode disturbance observer (FTSMDO) for disturbance estimation.
• Introduction of a fast nonsingular funnel error surface (FNFES) with hyperbolic tangent transformation.
• Integration of FNFES into a backstepping control framework, creating a fast funnel controller.
• Development of an improved nonlinear filter to mitigate the 'explosion of complexity' (EOC) issue.

Main Results:

• The proposed controller ensures consensus tracking errors converge to a prescribed boundary with small steady-state error.
• Fast convergence and reduced overshoot are achieved in tracking performance.
• The controller effectively handles unknown lumped disturbances, including internal uncertainties and external factors.
• Semi-global practical fixed-time stability (SPFS) of the closed-loop system is rigorously proven using Lyapunov theory.

Conclusions:

• The novel fixed-time control strategy offers superior performance for NMASs compared to existing methods.
• The approach successfully addresses disturbance rejection and stability concerns in nonlinear systems.
• Simulation results validate the effectiveness and robustness of the proposed control system.