Design of the optimal control of periodic processes in unlimited time

Consideration was given to the design of optimal control of periodic and oscillatory processes which are characteristics of the space applications where the time of control is not strictly limited and the limited resource is represented by the stock of the jet working fluid. The methods of the theory of singular relaxation extensions and the degenerate problems were used. In this case, solution has the form of the estimated minimizing sequence of positional controls which is constructed in the original class by approximating the permissible modes of the generalized solution, the cyclic sliding mode.