Reachable set of some discrete system with uncertain Liu disturbances

The paper considers the problem of finding the reachable set for a linear system with determinate and stochastic Liu's uncertainties. As Liu's uncertainties, we use uniformly distributed ordinary uncertain values defined in some uncertain space and independent of one another. This fact means that the state vector of the system becomes infinite-dimensional. As determinate uncertainties, we consider feedback controls and unknown initial states. Besides, there is a constraint in the form of a sum of uncertain expectations. The initial estimation problem reduces to a determinate multi-step problem for matrices with a fixed constraint at the right end of the trajectory. This reduction requires some information on Liu's theory. We give necessary and sufficient conditions for the finiteness of a target functional in the obtained determinate problem. We provide a numerical example of a two-dimensional two-step system.