Fixed-time sliding-mode distributed consensus and formation control of disturbed fractional-order multi-agent systems

Area of Science:

• Control Theory
• Systems Engineering
• Applied Mathematics

Background:

• Fractional-order multi-agent systems (FOMS) present unique control challenges.
• Achieving consensus and formation control in finite-time is crucial for coordinated behaviors.
• External disturbances can significantly impact system stability and performance.

Purpose of the Study:

• To investigate fixed-time consensus and formation control for FOMS.
• To address the impact of external disturbances on system performance.
• To develop a control strategy that guarantees finite-time convergence independent of initial states.

Main Methods:

• A novel distributed sliding-mode control (SMC) strategy is proposed.
• The control incorporates a neighborhood-based error variable for leader tracking.
• Fractional Lyapunov stability theorem is utilized for stability analysis and convergence time estimation.

Main Results:

• Fixed-time consensus and formation control are achieved for FOMS.
• The proposed control effectively handles external disturbances.
• The upper bound of convergence time is estimated and shown to be independent of initial conditions.

Conclusions:

• The developed distributed SMC method ensures fixed-time stability for FOMS.
• The approach is effective in achieving coordinated formation and consensus.
• Numerical simulations validate the efficacy of the proposed control design.