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Free-will arbitrary time optimization for multi-agent systems with time-varying function.

Jia Wu1, Wenyan Tang1, Wenzhong Lei1

  • 1School of Automation and Electronic Information, Xiangtan University, Xiangtan, China.

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|April 25, 2025
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Summary
This summary is machine-generated.

This study introduces novel distributed optimization strategies for multi-agent systems, enabling consensus and collective objective minimization within an arbitrary timeframe. These algorithms ensure agents reach agreement and optimize shared goals at a user-defined time.

Keywords:
Arbitrary timeMulti-agent systemsOptimizationTime-varying objective function

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Area of Science:

  • Control Theory
  • Distributed Systems
  • Optimization

Background:

  • Multi-agent systems require coordinated decision-making and objective optimization.
  • Existing methods often lack flexibility in specifying convergence time.
  • Arbitrary-time optimization presents a challenge for decentralized control.

Purpose of the Study:

  • To develop distributed optimization strategies for multi-agent systems with arbitrary settling times.
  • To ensure both consensus and collaborative minimization of time-varying objective functions.
  • To address the limitations of fixed-time and finite-time optimization.

Main Methods:

  • Developed distributed optimization algorithms for single-integrator and double-integrator multi-agent systems.
  • Utilized the zero-gradient-sum approach for algorithm design.
  • Leveraged the strongly convex nature of agent-specific time-varying functions.

Main Results:

  • The proposed algorithms achieve consensus among all agents.
  • Collective objective functions are minimized within a user-defined arbitrary time frame.
  • Theoretical analysis confirms the effectiveness of the developed strategies.

Conclusions:

  • The novel distributed strategies successfully enable arbitrary-time consensus and optimization in multi-agent systems.
  • The methods provide a flexible framework for coordinating agent behavior with precise temporal control.
  • Simulation results validate the theoretical findings and practical applicability.