On the Estimation Problem for One Class of Nonlinear Systems

Abstract

This paper considers the estimation problem for the state of one class of nonlinear multistage and continuous systems under uncertainty and with the quantities observed described by linear equations. It is assumed that the system's initial state and the disturbances in measurement equations are inexact, and that the allowable a priori information on these two is limited to their range of variation. The solution of the estimation problem relies on describing the evolution of the system's state information sets which are consistent with both the measurement results and the a priori restrictions on uncertain quantities. An information set consists of all trajectories that are possible in the system and which, together with certain admissible disturbances in the observation, determine the given realization of the observed signal. A cross-section, at some time-instant, of information sets generated by the signal observation prior to that instant, is a multiple-valued analog of the system's current phase condition. Information sets provide guaranteed estimates of the system's state based on measurement results.