What is Ellipsoidal Modelling and How to Use It for Control and State Estimation?

  • F. L. Chernousko
Part of the CISM Courses and Lectures book series (CISM, volume 388)


The paper is devoted to the overview of the method of ellipsoids for modelling and estimating uncertainties in dynamical systems. The method was developed during the last decades and belongs to the guaranteed (minimax or set-membership) approach to description of uncertain factors such as disturbances, measurement errors, indeterminate parameters, etc. By contrast to the well-known probabilistic approach, the guaranteed approach does not require precise knowledge of probability distributions (which are seldom available in practical problems) and yields reliable estimates for the system behavior. Whereas the guaranteed approach operates with the sets of uncertain parameters, the ellipsoidal technique essentially simplifies the estimation procedure by replacing general n-dimensional sets by their inner and outer ellipsoidal estimates. Thus, two-sided optimal estimates are obtained for reachable sets of dynamical systems. The fundamentals of the method of ellipsoids are presented, and the basic properties of the approximating ellipsoids are discussed. Various applications of the method to problems in control and state estimation are given.


Optimal Control Problem Differential Game Affine Transformation Admissible Control Outer Approximation 


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Copyright information

© Springer-Verlag Wien 1999

Authors and Affiliations

  • F. L. Chernousko
    • 1
  1. 1.Russian Academy of SciencesMoscowRussia

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