Аннотация:

The problem of controlling one-dimensional viscous gas flow through an interval with a fixed boundary is considered. The flow regime takes into account complex convective conductive radiative heat exchange in the medium. The heat transfer coefficient and the reflection coefficient at the boundaries are chosen to be controls. The existence of optimal control is proved. The necessary conditions for the optimality system are derived. A numerical solu-tion to the optimal control problem is calculated using the Physics Informed Neural Network (PINN) method. The method involves approximating an unknown function with a neural network by minimizing a quadratic functional that includes terms for the resi-duals of equations, boundary and initial conditions, and additional information. The method avoids the need for linearization and solving optimality systems.
The functions of velocity, density, tempe-rature, and radiation intensity are sought for boundary control with two coefficients on the left boundary and two coefficients on the right boundary. All unknowns are approximated by neural networks. The temperatures at observation points match the specified temperature using optimal control of the boundary coefficients. The case with observation points inside the region and on the boundaries is considered.