To probabilistic description of an ensemble of trajectories to a continuous-discrete control system with incomplete information

A linear control system with continuous and discrete times and discrete memory is considered. The model includes an uncertainty in the description of operators implementing control actions. This uncertainty is a consequence of random disturbances under the assumption of their uniform distribution over known intervals. With each implementation a corresponding trajectory arises from random perturbations, and in the aggregate - an ensemble of trajectories, for which a component-by-component probabilistic description is given in the form of a set of probability density functions parametrized by the current time. To construct these functions, the previously obtained representation of the Cauchy operator of the system under consideration is used. The proposed probabilistic description of perturbations for trajectory variables allows one to find their standard characteristics, including expectation and variance, as well as the entire possible range of values. The results are constructive in nature and allow for effective computer implementation. An illustrative example is given.