Dynamical Input Reconstruction Problem for a Quasi-Linear Stochastic System

作     者：Rozenberg, Valeriy L. 

作者机构：Krasovskii Institute of Mathematics and Mechanics Ural Branch of the Russian Academy of Sciences ul. S. Kovalevskoi 16 Yekaterinburg620990 Russia 

出 版 物：《IFAC-PapersOnLine》 

年 卷 期：2018年第51卷第32期

页      面：727-732页

核心收录：

主　　题：Inverse problems Covariance matrix Ordinary differential equations Random processes Stochastic models Stochastic systems Auxiliary modeling Discrete information Input reconstruction Mathematical expectation Quasi linear Simultaneous reconstruction Solving algorithm Theory of dynamics 

摘      要：The problem of reconstructing unknown inputs in a quasi-linear stochastic system with diffusion depending on the phase state is investigated by means of the approach of the theory of dynamic inversion. The statement when the simultaneous reconstruction of disturbances in the deterministic and stochastic terms of the system is performed from the discrete information on a number of realizations of the stochastic process is considered. The problem is reduced to an inverse problem for ordinary differential equations describing the mathematical expectation and covariance matrix of the process. A finite-step software-oriented solving algorithm based on the method of auxiliary controlled models is proposed. The key result of the paper is an estimate for the convergence rate of the algorithm with respect to the number of measurable realizations. © 2018