STOPPING TIMES AND PROBLEMS OF MOTION CORRECTION
This paper deals with using of optimal stopping times in problems of optimal correction of the motion. The theory of Markov optimal stopping times has been considered, for example, in [Shiryayev, 1978; Chow at al.,
1971]. In addition to that, a problem of motion correction for systems with incomplete information consists in the accumulation of measured data and the subsequent choice of a new control for remaining time interval. A determinate version of the problem of motion correction can be found in [Kurzhanski, 1977]. Here we consider multistage linear control systems with Gaussian noises and additive uncertainties. Using the results of convex analysis and the theory of Kalman filtering, we obtain the optimal minimax stopping times for the completion of observation and for the transition to a new control action. A simple one-dimensional example is examined for the purpose of an illustration. An application to the alignment problem in the theory of inertial navigation is also considered.