Fartushny I. Asymptotics of bounded separated controls in optimal parabolic periodic boundary value problems

The thesis is devoted to the construction of smooth asymptotics of solutions of optimal control problems for singular perturbed parabolic periodic systems with restrictions on controls. Three problems are considered: asymptotics of locally bounded optimal control for singular perturbed parabolic periodic boundary value problem for non-critical case, asymptotics of globally bounded optimal controls for singular perturbed parabolic periodic boundary value problem for critical case and asymptotics of minimax estimations for critical and degenerated problems. In the case of local restrictions on control numerical example is given, which shows the adjacency of constructed asymptotics, that is quality of asymptotics themselves. In the critical case of construction of asymptotics with global restrictions on control the conditions are found which allow to modify initial problem. Then this problem has bounded solutions with respect to small parameter . In critical and degenerated cases it was proved for solutions of minimax estimation the point is finite pole. For modified bounded value problems the asymptotics of arbitrary order of accuracy are constructed.