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Abstract
The ellipsoidal estimation of reachable sets is an efficient technique for the set-membership modelling of uncertain dynamical systems. In this paper, the optimal outer ellipsoidal approximation of reachable sets is considered, and attention is paid to the new criterion associated with the projection of the approximating ellipsoid onto a given direction. Nonlinear differential equations governing the evolution of ellipsoids are analysed and simplified. The asymptotic behaviour of ellipsoids near the initial point and at infinity is studied. It is shown that the optimal ellipsoids under consideration touch the corresponding reachable sets at all time instants. A control problem for a system subjected to uncertain perturbations is investigated in the framework of the optimal ellipsoidal estimation of reachable sets.
Acknowledgements
The work is partially supported by the Russian Foundation of Basic Research (Grant 05-01-00647) and by the Grant of the President of the RF for leading scientific schools No. 1627.2003.1.