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We consider the optimal control problem for a linear discrete stochastic system. The optimality criterion is the probability for the first coordinate of the system to fall into a given neighborhood of zero in time not exceeding a predefined value. The problem reduces to an equivalent stochastic optimal control problem with probabilistic terminal criterion. The latter can be solved analytically with dynamical programming. We give sufficient conditions for which the resulting optimal control turns out to be also optimal with respect to the quantile criterion.

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The correction problem of an aerial vehicle trajectory is considered. The mathematical model of the correction process is represented by a scalar stochastic control system with a probability terminal performance index. The system's state variable is the predicted miss of a single parameter of the aerial vehicle. It is assumed that the complete information about the state variable is available. The aim of the correction is to maximize the probability that the terminal miss does not exceed the pre scribed level. The execution errors of the designed correction impulse are distributed uniformly. Using dynamic programming, a procedure for the optimization of corrections of the aerial vehicle trajectory with respect to the probability performance index is developed, and this procedure is used to solve the one parameter optimal correction problem for the aerial vehicle for the case of N time steps. The resulting optimal control is compared to the known optimal controls with respect to other perfor mance indices.