Maximum principle of state-constrained optimal control governed by fluid dynamic systems
This work is concerned with optimal control of systems governed by three-dimensional Navier-Stokes equations which are non-well-posed, and the state constraint is of integral form. The authors define a penalty functional, via which they transform the original problem with the state constraint into another one called the approximate problem, which has no state constraint. Then they apply Ekeland's variational principle to find an optimal control pair for the approximate problem. By using the spike variation, they derive first-order necessary conditions for the optimal pair of the approximate problem; passing to the limit they obtain necessary conditions for the original optimal pair.
scientific article; zbMATH DE number 1891305