Synthesis of Optimal Control Progmm with Taking Account of Random Errors of its Realization

The paper discusses variational problems connected with synthesis of optimal, with respect to accuracy, program of bringing a controlled object to the desired phase state with taking account of random errors of its realization. The necessary and sufficient conditions of optimality are obtained. The analysis of functionals under consideration on optimal controls is made. It is shown that there exist control programs invariant to certain types of errors of their realization.