Motion correction of a statistically uncertain system under communication constraints

The problem of motion correction of a controlled system is considered. It is required to minimize a terminal functional under statistical uncertainty of the disturbance and incomplete information about the state of the system. Reachable sets of filtering and prediction equations are used; these sets are uniquely determined for a given time moment by the realizations of the observed signal and the chosen control. A modification of the correction problem under communication constraints is considered, in which the bounded capacity of the digital data transmission channel is taken into account. It is assumed that the object is equipped with a computing facility that can remember the measured information, process it with a high level of accuracy, transmit it, and receive encoded signals via communication channels. Signals in the form of words of bounded length consisting of integers come to the control and information processing center (CIPC) at discrete time moments. For simplicity, the communication channel is assumed to be noise- and delay-free. The encoding device in the communication channel is used for transmitting information about the measured parameters of the object to the CIPC and the control action from the CIPC to the object. At the CIPC, the information about the parameters is decoded and used for calculating the correction moments and optimal control. Relations between the reconstruction accuracy of the measured parameters and the optimal value of the functional are obtained as well as between the length of the transmitted word and the transmission frequency. Several results are exemplified.