ABOUT EQUIVALENCE BETWEEN CLOSED-LOOP AND OPEN-LOOP FEEDBACK CONTROLS.

Conditions of equivalence of the closed-loop CL and open-loop feedback OLF control strategies are formulated and proved. For the linear-quadratic LQ problem the conditions concern some covariance matrices of the estimation errors. It is shown that for some general class LQ Gaussian problems both the strategies are equivalent. The equivalence also exists in the case of LQ problem with complete state information and any disturbances in the form of stochastic processes of the second order.