Estimation of random information sets of multistep systems

Abstract

The estimation problems for the linear multistep controlled system under mixed perturbations are considered. It is assumed that deterministic perturbations are bounded by convex and compact constraints and random perturbations are Gaussian. Random information sets, called multiestimes for brevity, are defined. In the absence of random components, the introduced multiestimates coincide with information sets in the theory of guaranteed estimation. The multiestimate structure is considered. It is shown that multiestimates can be represented as the sum of a random vector and a deterministic set, which depend on several parameters. In turn, this set of parameters determines uniquely both conditional and unconditional probability of inclusion of the multiestimate in the covering set. Several special cases are analyzed, and the form of the covering set is discussed. A modification of the problem under communication constraints is proposed. This modification takes into account the limited capability of the digital data transfer channel. Relations between the accuracy of multiestimate parameters identification and the length of the transmitted word are obtained. A number of the obtained results are illustrated by examples.