Distributed optimization consensus for multi-agent systems on matrix-weighted networks

Area of Science:

• Control Theory
• Networked Systems
• Optimization

Background:

• Distributed optimization is crucial for coordinating multi-agent systems (MASs).
• Consensus problems in MASs are challenging, especially on complex network topologies.
• Existing methods may not fully address continuous-time (CT) and discrete-time (DT) dynamics simultaneously.

Purpose of the Study:

• To investigate distributed optimization consensus issues in first-order CT and DT MASs.
• To propose a novel matrix-weighted distributed optimization algorithm for these systems.
• To establish conditions for achieving optimization consensus.

Main Methods:

• Development of a new matrix-weighted distributed optimization algorithm.
• Application of Lyapunov stability theory for analysis.
• Utilisation of matrix theory to derive consensus conditions.

Main Results:

• The proposed algorithm facilitates optimization consensus in both CT and DT MASs.
• Formal conditions for achieving optimization consensus were derived using stability and matrix theories.
• Numerical examples validated the effectiveness of the proposed algorithm.

Conclusions:

• The developed algorithm effectively addresses distributed optimization consensus in MASs.
• The theoretical conditions derived provide a robust framework for system design.
• The findings are applicable to various networked control systems requiring coordinated optimization.