Rusina A. Approximate regulators in infinite-dimensional systems with rapidly oscillating coefficients

The thesis is devoted to the construction and justification of an approximate distributed optimal control in a feedback form of a number of the infinite-dimensional systems with rapidly oscillating coefficients. An approximate optimal control in a feedback form of optimal control problem of a parabolic equation with rapidly oscillating coefficients and distributed control on the right side and quadratic quality criteria on a finite time interval was build and justified. Two cases were considered: when impulse controlled perturbation of the system take place at a fixed moment of time and when control is bounded. Solution of the approximate optimal stabilization problem of a parabolic equation with rapidly oscillating coefficients was found in both cases of when impulse controlled perturbation of the system take place at a fixed moment of time and when control is bounded. An approximate optimal control in a feedback form of a hyperbolic equation with distributed control and rapidly oscillating coefficients was constructed and justified. The exact form of an optimal regulator of a parabolic system with lumped control and rapidly oscillating coefficients was found and his approximate form was justified.