On Equations of Ellipsoids Approximating Attainable Sets

A. I. Ovseevich
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A. I. Ovseevich: Russian Academy of Sciences

Journal of Optimization Theory and Applications, 1997, vol. 95, issue 3, No 10, 659-676

Abstract: Abstract This paper is devoted to a search for a guaranteed counterpart of the stochastic Kalman filter. We study the guaranteed filtering of a linear system such that the phase state and external disturbance form a vector subject to an ellipsoidal bound. This seemingly exotic setup can be justified by an analogy with the observation of Gaussian processes. Unfortunately, the resulting guaranteed filtering supplies us an ellipsoid approximating the localization domain for the state vector, but not the localization domain itself, and turns out to be more difficult compared to the Kalman filter. Our main results consist of an explicit evaluation of the Hamiltonians. In principle, this permits us to write explicitly the equations of the guaranteed filter.

Keywords: Kalman filter; guaranteed filtering; Hamiltonian equations; Bellman equation; ellipsoidal bounds (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022630107462

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