Automation and Remote Control

, Volume 62, Issue 3, pp 409–421 | Cite as

Decomposition of Nonlinear Stochastic Differential Systems

  • M. E. Shaikin
  • V. I. Shin


Decomposition of a system, i.e., representation of a system as a set of subsystems of lesser dimension, for a multivariate dynamic system described by a nonlinear Ito stochastic differential equation is investigated. The existence and explicit construction of coordinate systems (substitutions of variables) for decomposition are examined. Group-theoretic analysis of ordinary differential equations, which is effective for analyzing deterministic control systems, is also useful in studying the decomposition of stochastic systems. A relationship between the decompositions of the Ito stochastic system and its associated deterministic control system is determined. Examples are given.


Differential Equation Dynamic System Control System Coordinate System Mechanical Engineer 
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Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • M. E. Shaikin
    • 1
  • V. I. Shin
    • 2
  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia
  2. 2.Institute of Informatics ProblemsRussian Academy of SciencesMoscowRussia

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