Accelerating Fixed-Time Event-Triggered Optimization in Continuous and Discrete Time via Time-Varying Dynamical...

Area of Science:

• Control Systems Engineering
• Distributed Computing
• Optimization Theory

Background:

• Multiagent systems (MASs) require efficient distributed optimization protocols.
• Existing methods often struggle with convergence speed and communication overhead.
• Fixed-time control offers convergence in a finite, predetermined time.

Purpose of the Study:

• To develop a novel fixed-time protocol for distributed optimization in MASs.
• To enhance convergence speed and reduce communication overhead compared to existing methods.
• To extend the protocol to discrete-time systems while maintaining efficiency.

Main Methods:

• A two-stage fixed-time protocol design incorporating time-varying gain.
• Event-triggered communication for reduced overhead.
• Extension to discrete-time systems with a power-law decaying step-size.
• Rigorous mathematical analysis to ensure stability and robustness.

Main Results:

• Guaranteed fixed-time convergence independent of initial conditions.
• Significant acceleration of convergence (up to 778% faster).
• Reduction in communication overhead (up to 10.34%).
• Phased convergence in discrete-time settings with sustained savings.

Conclusions:

• The proposed fixed-time protocol offers superior performance for MAS distributed optimization.
• The event-triggered approach effectively reduces communication overhead.
• The discrete-time extension provides a practical and efficient solution for real-world applications.