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

This article proposes a novel approach using multi-task learning for solving nonlinear and complex optimal control problems. A neural network-based framework is proposed by unifying state, control, and adjoint dynamics into the three separate neural networks. A specific structure is designed to embed the Hamiltonian into a neural network framework for solving optimal control problems using the Pontryagin Maximum Principle. An iterative algorithm that synergizes specific structures is proposed for neural network learning sequentially and parallel. It is proved that the solution of neural networks converges to the main optimal control problem solution. This ensures that the Hamiltonian optimality condition is satisfied. To evaluate the current approach, two nonlinear complex optimal control problems in the field of epidemiology and power grid stabilization are solved successfully. Numerical results are given, and related graphs are depicted.