Distributed fixed/predefined-time optimization for multi-agent systems: new exponential-function-based algorithms.

Area of Science:

• Control Engineering
• Optimization Theory
• Multi-Agent Systems

Background:

• Distributed convex optimization is crucial for multi-agent systems (MASs).
• Existing methods face challenges in efficiency, restrictive assumptions, and computational complexity, especially for time-varying problems.
• Fixed/predefined-time convergence remains a significant hurdle.

Purpose of the Study:

• To develop innovative distributed optimization frameworks for MASs.
• To achieve efficient fixed/predefined-time convergence for both time-invariant and time-varying cost functions.
• To relax existing constraints and reduce computational complexity.

Main Methods:

• For time-invariant problems: An estimator-based two-stage distributed protocol ensuring inter-agent consensus and global optimum convergence.
• For time-varying problems: An enhanced zero-gradient-sum (ZGS) framework integrating zeroing neural networks (ZNN) with sliding mode control.
• Implicit Hessian inverse computation via ZNN dynamics to avoid high computational cost.

Main Results:

• The proposed protocol achieves fixed/predefined-time convergence for time-invariant problems with only strong convexity assumption on the global cost function.
• The enhanced ZGS framework eliminates dependence on initial conditions for time-varying problems.
• Methods demonstrate superior convergence speed and broad applicability in numerical simulations.

Conclusions:

• The developed frameworks offer efficient and robust solutions for distributed convex optimization in MASs.
• These methods significantly advance the state-of-the-art by addressing limitations of existing approaches.
• The research highlights the potential of ZNN and sliding mode control for complex optimization tasks.