Method of Inverse Dynamics Problems with Incomplete Observations

A dynamic object controlling problem is considered when the control algorithm is based on the concept of inverse problems of dynamics in conditions of incomplete observability of the state vector. It is shown that with the direct synthesis of control, the optimal value of the quality functional is achieved by measuring the full state vector. Otherwise, firstly, the closed control system will not meet the required restrictions, and, secondly, the conditions of optimality of the specified quality functional are not met. An algorithm for restoring the full state vector is proposed, the estimation of the state vector is determined as a function of the discrepancy, defined as the difference between the measurement vector and its forecast. This algorithm differs from the known ones in that the control signal is formed by the measured components of the state vector of the system, and the missing components are replaced by the coordinates of an ideal closed-loop system.