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Prescribed-time distributed optimization problem with constraints.

Hailong Li1, Miaomiao Zhang2, Zhongjie Yin1

  • 1Rocket Force University of Engineering, Xi'an 710025, PR China.

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|April 6, 2024
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Summary
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This study introduces new algorithms for distributed optimization problems, ensuring multi-agent systems reach optimal solutions within a set time, regardless of initial conditions.

Keywords:
Convex constraintConvex setDistributed optimizationPrescribed-time

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Area of Science:

  • Control Engineering
  • Distributed Systems
  • Optimization Theory

Background:

  • Distributed optimization problems are crucial in various fields.
  • Controlling multi-agent systems requires efficient optimization algorithms.

Purpose of the Study:

  • To develop algorithms for solving constrained and unconstrained distributed optimization problems within a prescribed time.
  • To ensure convergence time is independent of system parameters and initial states.

Main Methods:

  • Designed a prescribed-time distributed optimization algorithm with constraints using gradient projection and consensus algorithms.
  • Transformed constrained problems into unconstrained ones, proposing a new algorithm based on gradient descent and consensus.
  • Utilized appropriate objective functions to prove convergence properties.

Main Results:

  • Demonstrated that multi-agent systems can converge to the optimal solution within any prescribed time.
  • Proved that the convergence time is independent of initial conditions and system parameters.
  • Validated the algorithms through three simulation examples.

Conclusions:

  • The proposed algorithms effectively solve prescribed-time distributed optimization problems under constraints.
  • The developed methods offer robust and predictable convergence for multi-agent systems.
  • Simulation results confirm the practical applicability and validity of the designed algorithms.