Differential equations of ellipsoidal state estimates in nonlinear control problems under uncertainty

Tatiana Filippova

doi:10.3934/proc.2011.2011.410

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2011, Volume 2011: 410-419. Doi: 10.3934/proc.2011.2011.410 open access

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Differential equations of ellipsoidal state estimates in nonlinear control problems under uncertainty

Tatiana Filippova^1,

1.
Department of Optimal Control, Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 Sofia Kovalevskaya str., Ekaterinburg 620990

Received: June 30, 2010

Revised: January 31, 2011

Published: August 2017

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Abstract

The properties of set-valued states of differential control systems with uncertainties in initial data are considered. It is assumed that the dynamical system has a special structure, in which the nonlinear terms in the right-hand sides of related differential equations are quadratic in state coordinates. The model of uncertainty considered here is deterministic, with setmembership description of uncertain items which are taken to be unknown but bounded with given bounds. We construct external and internal ellipsoidal estimates of reachable sets of nonlinear control system and find differential equations of proposed ellipsoidal estimates of reachable sets of nonlinear control system. Numerical simulation results are also given.

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Mathematics Subject Classification: Primary: 34A60, 49J21; Secondary: 93C41, 49K21.

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