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Solving nonlinear and complex optimal control problems via multi-task artificial neural networks.

Ali Emami Kerdabadi1, Alaeddin Malek2

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This study introduces a new multi-task learning framework using neural networks to solve complex optimal control problems. The method ensures Hamiltonian optimality and is validated on epidemiology and power grid models.

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Area of Science:

  • Computational Mathematics
  • Control Theory
  • Artificial Intelligence

Background:

  • Optimal control problems are crucial in various scientific and engineering fields.
  • Solving nonlinear and complex optimal control problems remains a significant challenge.
  • Existing methods often struggle with high dimensionality and complex dynamics.

Purpose of the Study:

  • To propose a novel multi-task learning framework for solving nonlinear and complex optimal control problems.
  • To develop a unified neural network-based approach integrating state, control, and adjoint dynamics.
  • To ensure the satisfaction of the Hamiltonian optimality condition.

Main Methods:

  • A neural network framework is designed to unify state, control, and adjoint dynamics.
  • The Hamiltonian is embedded into the neural network structure using the Pontryagin Maximum Principle.
  • An iterative algorithm is proposed for sequential and parallel neural network learning.
  • Convergence of the neural network solution to the optimal control solution is proven.

Main Results:

  • The proposed framework successfully solves two nonlinear complex optimal control problems.
  • Applications include epidemiology modeling and power grid stabilization.
  • Numerical results and graphical representations demonstrate the approach's effectiveness.
  • The Hamiltonian optimality condition is satisfied by the neural network solutions.

Conclusions:

  • The multi-task learning framework offers an effective approach for complex optimal control.
  • The neural network integration provides a robust and convergent solution.
  • The method shows promise for real-world applications in diverse fields.